Английская Википедия:700 (number)

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Шаблон:Hatnote Шаблон:Infobox number 700 (seven hundred) is the natural number following 699 and preceding 701.

It is the sum of four consecutive primes (167 + 173 + 179 + 181), the perimeter of a Pythagorean triangle (75 + 308 + 317)[1] and a Harshad number.

Integers from 701 to 799

Nearly all of the palindromic integers between 700 and 800 (i.e. nearly all numbers in this range that have both the hundreds and units digit be 7) are used as model numbers for Boeing Commercial Airplanes.

700s

710s

720s

Шаблон:Main

730s

  • 730 = 2 × 5 × 73, sphenic number, nontotient, Harshad number, number of generalized weak orders on 5 points [30]
  • 731 = 17 × 43, sum of three consecutive primes (239 + 241 + 251), number of Euler trees with total weight 7 [31]
  • 732 = 22 × 3 × 61, sum of eight consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107), sum of ten consecutive primes (53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), Harshad number, number of collections of subsets of {1, 2, 3, 4} that are closed under union and intersection [32]
  • 733 = prime number, emirp, balanced prime,[33] permutable prime, sum of five consecutive primes (137 + 139 + 149 + 151 + 157)
  • 734 = 2 × 367, nontotient, number of traceable graphs on 7 nodes [34]
  • 735 = 3 × 5 × 72, Harshad number, Zuckerman number, smallest number such that uses same digits as its distinct prime factors
  • 736 = 25 × 23, centered heptagonal number,[35] happy number, nice Friedman number since 736 = 7 + 36, Harshad number
  • 737 = 11 × 67, palindromic number, blum integer.
  • 738 = 2 × 32 × 41, Harshad number.
  • 739 = prime number, strictly non-palindromic number,[36] lucky prime,[25] happy number, prime index prime

740s

  • 740 = 22 × 5 × 37, nontotient, number of connected squarefree graphs on 9 nodes [37]
  • 741 = 3 × 13 × 19, sphenic number, triangular number[3]
  • 742 = 2 × 7 × 53, sphenic number, decagonal number,[38] icosahedral number. It is the smallest number that is one more than triple its reverse. Lazy caterer number Шаблон:OEIS. Number of partitions of 30 into divisors of 30.[39]

Шаблон:Main

  • 743 = prime number, Sophie Germain prime, Chen prime, Eisenstein prime with no imaginary part

Шаблон:Main

  • 744 = 23 × 3 × 31, sum of four consecutive primes (179 + 181 + 191 + 193). It is the coefficient of the first degree term of the expansion of Klein's j-invariant. Furthermore, 744 =3 × 248 where 248 is the dimension of the Lie algebra E8.
  • 745 = 5 × 149 = 24 + 36, number of non-connected simple labeled graphs covering 6 vertices[40]
  • 746 = 2 × 373 = 15 + 24 + 36 = 17 + 24 + 36, nontotient, number of non-normal semi-magic squares with sum of entries equal to 6[41]
  • 747 = 32 × 83 = <math>\left\lfloor {\frac {4^{23}}{3^{23}}} \right\rfloor</math>,[42] palindromic number.
  • 748 = 22 × 11 × 17, nontotient, happy number, primitive abundant number[43]
  • 749 = 7 × 107, sum of three consecutive primes (241 + 251 + 257), blum integer

750s

  • 750 = 2 × 3 × 53, enneagonal number.[44]
  • 751 = prime number, Chen prime, emirp
  • 752 = 24 × 47, nontotient, number of partitions of 11 into parts of 2 kinds[45]
  • 753 = 3 × 251, blum integer
  • 754 = 2 × 13 × 29, sphenic number, nontotient, totient sum for first 49 integers, number of different ways to divide a 10 × 10 square into sub-squares [46]
  • 755 = 5 × 151, number of vertices in a regular drawing of the complete bipartite graph K9,9.[47]
  • 756 = 22 × 33 × 7, sum of six consecutive primes (109 + 113 + 127 + 131 + 137 + 139), pronic number,[2] Harshad number
  • 757 = prime number, palindromic prime, sum of seven consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127), happy number.
  • 758 = 2 × 379, nontotient, prime number of measurement [48]
  • 759 = 3 × 11 × 23, sphenic number, sum of five consecutive primes (139 + 149 + 151 + 157 + 163), a q-Fibonacci number for q=3 [49]

760s

770s

Шаблон:Main

780s

  • 780 = 22 × 3 × 5 × 13, sum of four consecutive primes in a quadruplet (191, 193, 197, and 199); sum of ten consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101), triangular number,[3] hexagonal number,[4] Harshad number
    • 780 and 990 are the fourth smallest pair of triangular numbers whose sum and difference (1770 and 210) are also triangular.
  • 781 = 11 × 71, sum of powers of 5/repdigit in base 5 (11111), Mertens function(781) = 0, lazy caterer number Шаблон:OEIS
  • 782 = 2 × 17 × 23, sphenic number, nontotient, pentagonal number,[13] Harshad number, also, 782 gear used by U.S. Marines
  • 783 = 33 × 29, heptagonal number
  • 784 = 24 × 72 = 282 = <math>1^3+2^3+3^3+4^3+5^3+6^3+7^3</math>, the sum of the cubes of the first seven positive integers, happy number
  • 785 = 5 × 157, Mertens function(785) = 0, number of series-reduced planted trees with 6 leaves of 2 colors [67]

Шаблон:Main

790s

References

Шаблон:Reflist

Шаблон:Integers Шаблон:Authority control

  1. Шаблон:Cite OEIS
  2. 2,0 2,1 Шаблон:Cite web
  3. 3,0 3,1 3,2 Шаблон:Cite web
  4. 4,0 4,1 Шаблон:Cite web
  5. Шаблон:Cite web
  6. 6,0 6,1 6,2 6,3 6,4 Шаблон:Cite web
  7. Шаблон:Cite OEIS
  8. Шаблон:Cite OEIS
  9. Шаблон:Cite journal
  10. Шаблон:Cite OEIS
  11. Шаблон:Cite OEIS
  12. Шаблон:Cite OEIS
  13. 13,0 13,1 Шаблон:Cite web
  14. Шаблон:Cite web
  15. Шаблон:Cite web
  16. 16,0 16,1 Шаблон:Cite web
  17. Шаблон:Cite web
  18. Шаблон:Cite web
  19. Шаблон:Cite OEIS
  20. Шаблон:Cite OEIS
  21. Шаблон:Cite OEIS
  22. Шаблон:Cite OEIS
  23. Шаблон:Cite OEIS
  24. Шаблон:Cite web
  25. 25,0 25,1 25,2 25,3 Шаблон:Cite web
  26. Шаблон:Cite web
  27. Шаблон:Cite OEIS
  28. Шаблон:Cite web
  29. Шаблон:Cite web
  30. Шаблон:Cite OEIS
  31. Шаблон:Cite OEIS
  32. Шаблон:Cite OEIS
  33. Шаблон:Cite web
  34. Шаблон:Cite OEIS
  35. Шаблон:Cite web
  36. Шаблон:Cite web
  37. Шаблон:Cite OEIS
  38. Шаблон:Cite web
  39. Шаблон:Cite OEIS
  40. Шаблон:Cite OEIS
  41. Шаблон:Cite OEIS
  42. Шаблон:Cite OEIS
  43. Шаблон:Cite web
  44. Шаблон:Cite web
  45. Шаблон:Cite OEIS
  46. Шаблон:Cite OEIS
  47. Шаблон:Cite OEIS
  48. Шаблон:Cite OEIS
  49. Шаблон:Cite OEIS
  50. Шаблон:Cite web
  51. Шаблон:Cite web
  52. Шаблон:Cite OEIS
  53. Шаблон:Cite OEIS
  54. Шаблон:Cite web
  55. Шаблон:Cite OEIS
  56. Шаблон:Cite web
  57. Шаблон:Cite OEIS
  58. Шаблон:Cite web
  59. Шаблон:Cite OEIS
  60. Шаблон:Cite OEIS
  61. Шаблон:Cite web
  62. Шаблон:Cite web
  63. Шаблон:OEIS
  64. Шаблон:Cite web
  65. Шаблон:Cite web
  66. Шаблон:Cite web
  67. Шаблон:Cite OEIS
  68. Шаблон:Cite OEIS
  69. Шаблон:Cite OEIS
  70. Шаблон:Cite OEIS
  71. Шаблон:Cite OEIS
  72. Шаблон:Cite OEIS
  73. Шаблон:Cite OEIS
  74. Шаблон:Cite OEIS
  75. Шаблон:Cite OEIS