Английская Википедия:800 (number)

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Шаблон:Redirect Шаблон:Redirect-multi Шаблон:Infobox number 800 (eight hundred) is the natural number following 799 and preceding 801.

It is the sum of four consecutive primes (193 + 197 + 199 + 211). It is a Harshad number, an Achilles number and the area of a square with diagonal 40.[1]

Integers from 801 to 899

800s

Шаблон:Main

810s

820s

  • 820 = 22 × 5 × 41, triangular number, smallest triangular number that starts with the digit 8[20] Harshad number, happy number, repdigit (1111) in base 9
  • 821 = prime number, twin prime, Chen prime, Eisenstein prime with no imaginary part, lazy caterer number Шаблон:OEIS, prime quadruplet with 823, 827, 829
  • 822 = 2 × 3 × 137, sum of twelve consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97), sphenic number, member of the Mian–Chowla sequence[21]
  • 823 = prime number, twin prime, lucky prime, the Mertens function of 823 returns 0, prime quadruplet with 821, 827, 829
  • 824 = 23 × 103, refactorable number, sum of ten consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103), the Mertens function of 824 returns 0, nontotient
  • 825 = 3 × 52 × 11, Smith number,[22] the Mertens function of 825 returns 0, Harshad number
  • 826 = 2 × 7 × 59, sphenic number, number of partitions of 29 into parts each of which is used a different number of times[23]
  • 827 = prime number, twin prime, part of prime quadruplet with {821, 823, 829}, sum of seven consecutive primes (103 + 107 + 109 + 113 + 127 + 131 + 137), Chen prime, Eisenstein prime with no imaginary part, strictly non-palindromic number[24]
  • 828 = 22 × 32 × 23, Harshad number, triangular matchstick number[25]
  • 829 = prime number, twin prime, part of prime quadruplet with {827, 823, 821}, sum of three consecutive primes (271 + 277 + 281), Chen prime, centered triangular number

830s

  • 830 = 2 × 5 × 83, sphenic number, sum of four consecutive primes (197 + 199 + 211 + 223), nontotient, totient sum for first 52 integers
  • 831 = 3 × 277, number of partitions of 32 into at most 5 parts[26]
  • 832 = 26 × 13, Harshad number, member of the sequence Horadam(0, 1, 4, 2)[27]
  • 833 = 72 × 17, octagonal number Шаблон:OEIS, a centered octahedral number[28]
  • 834 = 2 × 3 × 139, cake number, sphenic number, sum of six consecutive primes (127 + 131 + 137 + 139 + 149 + 151), nontotient
  • 835 = 5 × 167, Motzkin number[29]

Шаблон:Main

  • 836 = 22 × 11 × 19, weird number
  • 837 = 33 × 31, the 36th generalized heptagonal number[30]
  • 838 = 2 × 419, palindromic number, number of distinct products ijk with 1 <= i<j<k <= 23[31]
  • 839 = prime number, safe prime,[32] sum of five consecutive primes (157 + 163 + 167 + 173 + 179), Chen prime, Eisenstein prime with no imaginary part, highly cototient number[33]

840s

Шаблон:Main

  • 840 = 23 × 3 × 5 × 7, highly composite number,[34] smallest number divisible by the numbers 1 to 8 (lowest common multiple of 1 to 8), sparsely totient number,[35] Harshad number in base 2 through base 10, idoneal number, balanced number,[36] sum of a twin prime (419 + 421). With 32 distinct divisors, it is the number below 1000 with the largest amount of divisors.
  • 841 = 292 = 202 + 212, sum of three consecutive primes (277 + 281 + 283), sum of nine consecutive primes (73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109), centered square number,[37] centered heptagonal number,[38] centered octagonal number[39]
  • 842 = 2 × 421, nontotient, 842!! - 1 is prime,[40] number of series-reduced trees with 18 nodes[41]
  • 843 = 3 × 281, Lucas number[42]
  • 844 = 22 × 211, nontotient, smallest 5 consecutive integers which are not squarefree are: 844 = 22 × 211, 845 = 5 × 132, 846 = 2 × 32 × 47, 847 = 7 × 112 and 848 = 24 × 53 [43]
  • 845 = 5 × 132, concentric pentagonal number,[44] number of emergent parts in all partitions of 22 [45]
  • 846 = 2 × 32 × 47, sum of eight consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113 + 127), nontotient, Harshad number
  • 847 = 7 × 112, happy number, number of partitions of 29 that do not contain 1 as a part[46]
  • 848 = 24 × 53, untouchable number
  • 849 = 3 × 283, the Mertens function of 849 returns 0, blum integer

850s

860s

  • 860 = 22 × 5 × 43, sum of four consecutive primes (199 + 211 + 223 + 227), Hoax number[57]
  • 861 = 3 × 7 × 41, sphenic number, triangular number,[20] hexagonal number,[58] Smith number[22]
  • 862 = 2 × 431, lazy caterer number Шаблон:OEIS
  • 863 = prime number, safe prime,[32] sum of five consecutive primes (163 + 167 + 173 + 179 + 181), sum of seven consecutive primes (107 + 109 + 113 + 127 + 131 + 137 + 139), Chen prime, Eisenstein prime with no imaginary part, index of prime Lucas number[59]
  • 864 = 25 × 33, Achilles number, sum of a twin prime (431 + 433), sum of six consecutive primes (131 + 137 + 139 + 149 + 151 + 157), Harshad number
  • 865 = 5 × 173,
  • 866 = 2 × 433, nontotient, number of one-sided noniamonds,[60] number of cubes of edge length 1 required to make a hollow cube of edge length 13
  • 867 = 3 × 172, number of 5-chromatic simple graphs on 8 nodes[61]
  • 868 = 22 × 7 × 31 = J3(10),[62] nontotient
  • 869 = 11 × 79, the Mertens function of 869 returns 0

870s

  • 870 = 2 × 3 × 5 × 29, sum of ten consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107), pronic number,[13] nontotient, sparsely totient number,[35] Harshad number
  • 871 = 13 × 67, thirteenth tridecagonal number
  • 872 = 23 × 109, refactorable number, nontotient, 872! + 1 is prime
  • 873 = 32 × 97, sum of the first six factorials from 1
  • 874 = 2 × 19 × 23, sphenic number, sum of the first twenty-three primes, sum of the first seven factorials from 0, nontotient, Harshad number, happy number
  • 875 = 53 × 7, unique expression as difference of positive cubes:[63] 103 - 53
  • 876 = 22 × 3 × 73, generalized pentagonal number[64]
  • 877 = prime number, Bell number,[65] Chen prime, the Mertens function of 877 returns 0, strictly non-palindromic number,[24] prime index prime
  • 878 = 2 × 439, nontotient, number of Pythagorean triples with hypotenuse < 1000.[66]
  • 879 = 3 × 293, number of regular hypergraphs spanning 4 vertices,[67] candidate Lychrel seed number

880s

Шаблон:Main

  • 880 = 24 × 5 × 11 = 11!!!,[68] Harshad number; 148-gonal number; the number of n×n magic squares for n = 4.
    • country calling code for Bangladesh

Шаблон:Main

  • 881 = prime number, twin prime, sum of nine consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113), Chen prime, Eisenstein prime with no imaginary part, happy number
  • 882 = 2 × 32 × 72 = <math>\binom{9}{5}_2</math> a trinomial coefficient,[69] Harshad number, totient sum for first 53 integers, area of a square with diagonal 42[1]
  • 883 = prime number, twin prime, sum of three consecutive primes (283 + 293 + 307), the Mertens function of 883 returns 0
  • 884 = 22 × 13 × 17, the Mertens function of 884 returns 0, number of points on surface of tetrahedron with sidelength 21[70]
  • 885 = 3 × 5 × 59, sphenic number, number of series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of 7.[71]
  • 886 = 2 × 443, the Mertens function of 886 returns 0
    • country calling code for Taiwan
  • 887 = prime number followed by primal gap of 20, safe prime,[32] Chen prime, Eisenstein prime with no imaginary part
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Шаблон:Main

  • 888 = 23 × 3 × 37, sum of eight consecutive primes (97 + 101 + 103 + 107 + 109 + 113 + 127 + 131), Harshad number, strobogrammatic number,[9] happy number, 888!! - 1 is prime[72]
  • 889 = 7 × 127, the Mertens function of 889 returns 0

890s

  • 890 = 2 × 5 × 89 = 192 + 232 (sum of squares of two successive primes),[73] sphenic number, sum of four consecutive primes (211 + 223 + 227 + 229), nontotient
  • 891 = 34 × 11, sum of five consecutive primes (167 + 173 + 179 + 181 + 191), octahedral number
  • 892 = 22 × 223, nontotient, number of regions formed by drawing the line segments connecting any two perimeter points of a 6 times 2 grid of squares like this Шаблон:OEIS.
  • 893 = 19 × 47, the Mertens function of 893 returns 0
    • Considered an unlucky number in Japan, because its digits read sequentially are the literal translation of yakuza.
  • 894 = 2 × 3 × 149, sphenic number, nontotient
  • 895 = 5 × 179, Smith number,[22] Woodall number,[74] the Mertens function of 895 returns 0
  • 896 = 27 × 7, refactorable number, sum of six consecutive primes (137 + 139 + 149 + 151 + 157 + 163), the Mertens function of 896 returns 0
  • 897 = 3 × 13 × 23, sphenic number, cullen number Шаблон:OEIS
  • 898 = 2 × 449, the Mertens function of 898 returns 0, nontotient
  • 899 = 29 × 31 (a twin prime product),[75] happy number, smallest number with digitsum 26,[76] number of partitions of 51 into prime parts

References

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