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900 (number)

From Wikipedia, the free encyclopedia
For the year 900, see 900 BC and 900 AD.
"976 (number)" redirects here. Not to be confused with 976 number.
← 899 900 901 ⊟
Cardinalnine hundred
Ordinal900th
(nine hundredth)
Factorization22 × 32 × 52
Divisors1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
Greek numeralϠ´
Roman numeralCM
Binary11100001002
Ternary10201003
Senary41006
Octal16048
Duodecimal63012
Hexadecimal38416
ArmenianՋ
Hebrewתת"ק / ץ
Babylonian cuneiform𒌋𒐙
Egyptian hieroglyph𓍪

900 (nine hundred) is the natural number following 899 and preceding 901. It is the square of 30 and the sum of Euler's totient function for the first 54 positive integers. In base 10, it is a Harshad number. It is also the first number to be the square of a sphenic number.

In other fields

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900 is also:

Integers from 901 to 999

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900s

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910s

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  • 910 = 2 × 5 × 7 × 13, Mertens function(910) returns 0, Harshad number, happy number, balanced number,[8] number of polynomial symmetric functions of matrix of order 7 under separate row and column permutations[9]
  • 911 = Sophie Germain prime number, also the emergency telephone number in North America
  • 912 = 24 × 3 × 19, sum of four consecutive primes (223 227 229 233), sum of ten consecutive primes (71 73 79 83 89 97 101 103 107 109), Harshad number.
  • 913 = 11 × 83, Smith number,[10] Mertens function(913) returns 0.
  • 914 = 2 × 457, nontotient, number of compositions of 11 that are neither weakly increasing nor weakly decreasing [11]
  • 915 = 3 × 5 × 61, sphenic number, Smith number,[10] Mertens function(915) returns 0, Harshad number
  • 916 = 22 × 229, Mertens function(916) returns 0, nontotient, strobogrammatic, member of the Mian–Chowla sequence[12]
  • 917 = 7 × 131, sum of five consecutive primes (173 179 181 191 193)
  • 918 = 2 × 33 × 17, Harshad number
  • 919 = prime number, cuban prime,[13] prime index prime, Chen prime, palindromic prime, centered hexagonal number,[14] Mertens function(919) returns 0

920s

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930s

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  • 930 = 2 × 3 × 5 × 31, pronic number[23]
  • 931 = 72 × 19; sum of three consecutive primes (307 311 313); double repdigit, 11130 and 77711; number of regular simple graphs spanning 7 vertices [24]
  • 932 = 22 × 233, number of regular simple graphs on 7 labeled nodes [25]
  • 933 = 3 × 311
  • 934 = 2 × 467, nontotient
  • 935 = 5 × 11 × 17, sphenic number, Lucas–Carmichael number,[26] Harshad number
  • 936 = 23 × 32 × 13, pentagonal pyramidal number,[27] Harshad number
  • 937 = prime number, Chen prime, star number,[28] happy number
  • 938 = 2 × 7 × 67, sphenic number, nontotient, number of lines through at least 2 points of an 8 × 8 grid of points [29]
  • 939 = 3 × 313, number of V-toothpicks after 31 rounds of the honeycomb sequence [30]

940s

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950s

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  • 950 = 2 × 52 × 19, nontotient, generalized pentagonal number[41]
    • one of two ISBN Group Identifiers for books published in Argentina
  • 951 = 3 × 317, centered pentagonal number[42]
    • one of two ISBN Group Identifiers for books published in Finland
  • 952 = 23 × 7 × 17, number of reduced words of length 3 in the Weyl group D_17,[43] number of regions in regular tetradecagon with all diagonals drawn. [44]
    • 952 is also 9-5-2, a card game similar to bridge.
    • one of two ISBN Group Identifiers for books published in Finland
  • 953 = prime number, Sophie Germain prime,[45] Chen prime, Eisenstein prime with no imaginary part, centered heptagonal number[46]
    • ISBN Group Identifier for books published in Croatia
  • 954 = 2 × 32 × 53, sum of ten consecutive primes (73 79 83 89 97 101 103 107 109 113), nontotient, Harshad number, sixth derivative of x^(x^x) at x=1.[47]
  • 955 = 5 × 191, number of transitive rooted trees with 17 nodes
    • ISBN Group Identifier for books published in Sri Lanka
  • 956 = 22 × 239, number of compositions of 13 into powers of 2.[48]
    • ISBN Group Identifier for books published in Chile
  • 957 = 3 × 11 × 29, sphenic number, antisigma(45)[49]
    • one of two ISBN Group Identifiers for books published in Taiwan and China
  • 958 = 2 × 479, nontotient, Smith number[10]
  • 959 = 7 × 137, composite de Polignac number[50]
    • ISBN Group Identifier for books published in Cuba

960s

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  • 960 = 26 × 3 × 5, sum of six consecutive primes (149 151 157 163 167 173), Harshad number
    • country calling code for Maldives, ISBN Group Identifier for books published in Greece
    • The number of possible starting positions for the chess variant Chess960
  • 961 = 312, the largest 3-digit perfect square, sum of three consecutive primes (313 317 331), sum of five consecutive primes (181 191 193 197 199), centered octagonal number[51]
    • country calling code for Lebanon, ISBN Group Identifier for books published in Slovenia
  • 962 = 2 × 13 × 37, sphenic number, nontotient
    • country calling code for Jordan, one of two ISBN Group Identifiers for books published in Hong Kong
  • 963 = 32 × 107, sum of the first twenty-four primes
    • country calling code for Syria, ISBN Group Identifier for books published in Hungary
  • 964 = 22 × 241, sum of four consecutive primes (233 239 241 251), nontotient, totient sum for first 56 integers
    • country calling code for Iraq, ISBN Group Identifier for books published in Iran, happy number
  • 965 = 5 × 193
    • country calling code for Kuwait, ISBN Group Identifier for books published in Israel
  • 966 = 2 × 3 × 7 × 23 = , sum of eight consecutive primes (103 107 109 113 127 131 137 139), Harshad number
    • country calling code for Saudi Arabia, one of two ISBN Group Identifiers for books published in Ukraine
  • 967 = prime number, prime index prime
    • country calling code for Yemen, one of two ISBN Group Identifiers for books published in Malaysia
  • 968 = 23 × 112, nontotient, Achilles number, area of a square with diagonal 44[52]
    • country calling code for Oman, one of two ISBN Group Identifiers for books published in Mexico
  • 969 = 3 × 17 × 19, sphenic number, nonagonal number,[53] tetrahedral number[54]

970s

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  • 970 = 2 × 5 × 97, sphenic number, heptagonal number
    • country calling code for Palestinian territories, one of two ISBN Group Identifiers for books published in Mexico
  • 971 = prime number, Chen prime, Eisenstein prime with no imaginary part
    • country calling code for United Arab Emirates, ISBN Group Identifier for books published in the Philippines
  • 972 = 22 × 35, Harshad number, Achilles number
    • country calling code for Israel, one of two ISBN Group Identifiers for books published in Portugal
      • The Sum of Anti-Factors of 972 = number * (n/2) where n is an Odd number. So, it is a Hemi-Anti-Perfect Number. Other such Numbers include 2692, etc.

972 has Anti-Factors = 5, 8, 24, 29, 67, 72, 216, 389, 648

Sum of Anti-Factors = 5 8 24 29 67 72 216 389 648 = 1458 = 972 * 3/2

  • 973 = 7 × 139, happy number
    • country calling code for Bahrain, ISBN Group Identifier for books published in Romania,
  • 974 = 2 × 487, nontotient, 974! - 1 is prime[55]
    • country calling code for Qatar, ISBN Group Identifier for books published in Thailand
  • 975 = 3 × 52 × 13
    • country calling code for Bhutan, ISBN Group Identifier for books published in Turkey
  • 976 = 24 × 61, decagonal number[56]
  • 977 = prime number, sum of nine consecutive primes (89 97 101 103 107 109 113 127 131), balanced prime,[39] Chen prime, Eisenstein prime with no imaginary part, Stern prime,[57] strictly non-palindromic number[58]
    • country calling code for Nepal
    • EAN prefix for ISSNs
    • ISBN Group Identifier for books published in Egypt
  • 978 = 2 × 3 × 163, sphenic number, nontotient, number of secondary structures of RNA molecules with 11 nucleotides[59]
    • First EAN prefix for ISBNs
    • ISBN Group Identifier for books published in Nigeria
  • 979 = 11 × 89, the sum of the five smallest fourth powers:
    • Second EAN prefix for ISBNs. Also for ISMNs
    • ISBN Group Identifier for books published in Indonesia

980s

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990s

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  • 990 = 2 × 32 × 5 × 11, sum of six consecutive primes (151 157 163 167 173 179), triangular number,[3] Harshad number
  • 991 = prime number, sum of five consecutive primes (191 193 197 199 211), sum of seven consecutive primes (127 131 137 139 149 151 157), Chen prime, lucky prime, prime index prime
  • 992 = 25 × 31, pronic number,[23] nontotient; number of eleven-dimensional exotic spheres.[68]
    • country calling code for Tajikistan
  • 993 = 3 × 331
    • country calling code for Turkmenistan
  • 994 = 2 × 7 × 71, sphenic number, nontotient, number of binary words of length 13 with all distinct runs.[69]
    • country calling code for Azerbaijan
  • 995 = 5 × 199
    • country calling code for Georgia
    • Singapore fire brigade and emergency ambulance services hotline, Brunei Darussalam fire service emergency number
  • 996 = 22 × 3 × 83
    • country calling code for Kyrgyzstan
  • 997 = largest three-digit prime number, strictly non-palindromic number.[58] It is also a lucky prime.
  • 998 = 2 × 499, nontotient, number of 7-node graphs with two connected components.[70]
    • country calling code for Uzbekistan
Main article: 999 (number)

References

[edit]
Wikimedia Commons has media related to 900 (number).
  1. ^ "Pay-Per-Call Information Services". Federal Communications Commission. 2011-02-11. Retrieved 2021-03-31.
  2. ^ "Bowler throws 36 consecutive strikes for incredible 900 series". For The Win. 2016-01-13. Retrieved 2021-03-31.
  3. ^ a b c "Sloane's A000217: Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A036469 (Partial sums of A000009 (partitions into distinct parts))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ "Sloane's A098237: Composite de Polignac numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-10.
  6. ^ a b Sloane, N. J. A. (ed.). "Sequence A006245 (Number of primitive sorting networks on n elements; also number of rhombic tilings of a 2n-gon)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
  7. ^ Sloane, N. J. A. (ed.). "Sequence A303546 (Number of non-isomorphic aperiodic multiset partitions of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
  8. ^ Sloane, N. J. A. (ed.). "Sequence A020492 (Balanced numbers: numbers k such that phi(k) (A000010) divides sigma(k) (A000203))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  9. ^ Sloane, N. J. A. (ed.). "Sequence A007716 (Number of polynomial symmetric functions of matrix of order n under separate row and column permutations)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  10. ^ a b c d e "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  11. ^ Sloane, N. J. A. (ed.). "Sequence A332834 (Number of compositions of n that are neither weakly increasing nor weakly decreasing)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
  12. ^ "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  13. ^ "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  14. ^ "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  15. ^ Sloane, N. J. A. (ed.). "Sequence A055544 (Total number of nodes in all rooted trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
  16. ^ Sloane, N. J. A. (ed.). "Sequence A301462 (Number of enriched r-trees of size n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
  17. ^ Sloane, N. J. A. (ed.). "Sequence A030662 (Number of combinations of n things from 1 to n at a time, with repeats allowed)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
  18. ^ "Sloane's A000984 : Central binomial coefficients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  19. ^ "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  20. ^ "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  21. ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  22. ^ "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  23. ^ a b "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  24. ^ Sloane, N. J. A. (ed.). "Sequence A319612 (Number of regular simple graphs spanning n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-23.
  25. ^ Sloane, N. J. A. (ed.). "Sequence A295193 (Number of regular simple graphs on n labeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
  26. ^ "Sloane's A006972 : Lucas-Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  27. ^ "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  28. ^ "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  29. ^ Sloane, N. J. A. (ed.). "Sequence A018808 (Number of lines through at least 2 points of an n X n grid of points)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-22.
  30. ^ Sloane, N. J. A. (ed.). "Sequence A161206 (V-toothpick (or honeycomb) sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  31. ^ Sloane, N. J. A. (ed.). "Sequence A001628 (Convolved Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  32. ^ Sloane, N. J. A. (ed.). "Sequence A005727". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  33. ^ "Sloane's A006882 : Double factorials". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  34. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 13. ISBN 978-1-84800-000-1.
  35. ^ "Sloane's A006038 : Odd primitive abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  36. ^ "Sloane's A006036 : Primitive pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  37. ^ "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  38. ^ "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  39. ^ a b "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  40. ^ Sloane, N. J. A. (ed.). "Sequence A269134 (Number of combinatory separations of normal multisets of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-13.
  41. ^ Sloane, N. J. A. (ed.). "Sequence A001318 (Generalized pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  42. ^ "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  43. ^ Sloane, N. J. A. (ed.). "Sequence A162328 (Number of reduced words of length n in the Weyl group D_17)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-12.
  44. ^ Sloane, N. J. A. (ed.). "Sequence A007678 (Number of regions in regular n-gon with all diagonals drawn.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-13.
  45. ^ "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  46. ^ "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  47. ^ Sloane, N. J. A. (ed.). "Sequence A179230". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-12.
  48. ^ (sequence A023359 in the OEIS)
  49. ^ Sloane, N. J. A. (ed.). "Sequence A024816 (Antisigma(n): Sum of the numbers less than n that do not divide n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-11.
  50. ^ "Sloane's A098237: Composite de Polignac numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-10.
  51. ^ "Sloane's A016754 : Odd squares: a(n) = (2n 1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  52. ^ Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  53. ^ "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  54. ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  55. ^ "A002982: Numbers n such that n! - 1 is prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-10.
  56. ^ "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  57. ^ "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  58. ^ a b c "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  59. ^ Sloane, N. J. A. (ed.). "Sequence A004148 (Generalized Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  60. ^ "A008793". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-10.
  61. ^ "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  62. ^ "Sloane's A001190 : Wedderburn-Etherington numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  63. ^ "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  64. ^ "Sloane's A000129 : Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  65. ^ Sloane, N. J. A. (ed.). "Sequence A006330 (Number of corners, or planar partitions of n with only one row and one column)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  66. ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  67. ^ "Sloane's A0217719 : Extra strong Lucas pseudoprimes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-11.
  68. ^ "week164". Math.ucr.edu. 2001-01-13. Retrieved 2014-05-12.
  69. ^ "A351016". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-10.
  70. ^ "A275165". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-10.
  71. ^ "Sloane's A006886 : Kaprekar numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.
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