818

Integers from 801 to 899

800s

801 is a Harshad number. 801 is the sum of a square and positive cube in more than one way, and a sum of distinct positive cubes in more than one way:

801

=

17

2

+

8

3

=

26

2

+

5

3

=

1

3

+

2

3

+

4

3

+

6

3

+

8

3

=

2

3

+

4

3

+

9

810s

810 = 2 × 34 × 5. It is a harshad number. There are 810 non-equivalent ways of expressing 100,000 as the sum of two prime numbers. There are 810 distinct reduced words of length 5 in the Coxeter group of "Apollonian reflections" in three dimensions.

811 is a prime number, a twin prime, a Chen prime, the largest minimal prime in base 9, and the sum of five consecutive primes (151 + 157 + 163 + 167 + 173). It is a happy number and a zero of Mertens function.

812 = 22 × 7 × 29. It is an admirable number, a pronic number, a balanced number, and a zero of Mertens function.

813 = 3 × 271. It is a Blum integer.

814 = 2 × 11 × 37. It is a sphenic number, a nontotient, and a zero of Mertens function. There are 814 fixed hexahexes.

815 = 5 × 163. There are 815 graphs with 8 vertices and a distinguished bipartite block.

816 = 24 × 3 × 17. It is a tetrahedral number, a Padovan number, and a Zuckerman number.

817 = 19 × 43. It is a centered hexagonal number and the sum of three consecutive primes (269 + 271 + 277).

818 = 2 × 409. It is a nontotient and a strobogrammatic number

819 = 32 × 7 × 13. It is a square pyramidal number.

820s

820 = 22 × 5 × 41. It is a Harshad number, a happy number, a repdigit (1111) in base 9, and the 40th triangular number.

821 is a prime number, a twin prime, a Chen prime, and an Eisenstein prime with no imaginary part. It forms a prime quadruplet with 823, 827, and 829. It is a lazy caterer number.

822 = 2 × 3 × 137. It is a sphenic number, a member of the Mian–Chowla sequence, and the sum of twelve consecutive primes (43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97).

823 is a prime number, a twin prime, and a lucky prime. It forms a prime quadruplet with 821, 827, and 829. It is a zero of Mertens function.

824 = 23 × 103, refactorable number, nontotient, a zero of Mertens function, and the sum of ten consecutive primes (61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103).

825 = 3 × 52 × 11. It is a Smith number, a Harshad number, and a zero of Mertens function.

826 = 2 × 7 × 59. It is a sphenic number. There are 825 partitions of 29 into parts each of which is used a different number of times.

827 is a prime number, a twin prime, a Chen prime, a Eisenstein prime with no imaginary part, and the sum of seven consecutive primes (103 + 107 + 109 + 113 + 127 + 131 + 137). It forms a prime quadruplet with 821, 823, and 829. It is a strictly non-palindromic number.

828 = 22 × 32 × 23. It is a Harshad number and a triangular matchstick number.

829 is a prime number, a twin prime, a Chen prime, and the sum of three consecutive primes (271 + 277 + 281). It forms a prime quadruplet with 821, 823, and 827. It is a centered triangular number.

830s

830 = 2 × 5 × 83. It is a sphenic number, a nontotient, the totient sum of the first 52 integers, and the sum of four consecutive primes (197 + 199 + 211 + 223).

831 = 3 × 277. There are 831 partitions of 32 into at most 5 parts.

832 = 26 × 13. It is a Harshad number and a member of the Horadam sequence (0,1,4,2).

833 = 72 × 17. It is an octagonal number and a centered octahedral number.

834 = 2 × 3 × 139. It is a cake number, a sphenic number, a nontotient, and the sum of six consecutive primes (127 + 131 + 137 + 139 + 149 + 151).

835 = 5 × 167. It is a Motzkin number.

The factorization of 836 is 22 × 11 × 19, so its proper factors are 1, 2, 4, 11, 19, 22, 38, 44, 76, 209, and 418. They sum to 844. As this is greater than 836, it is an abundant number, but no subset sums to 836, so it is not a semiperfect number; therefore it is a weird number. Besides, 836 is the smallest weird number that is also an untouchable number, i.e. there is no n such that the sum of proper factors of n equals 836. (The only smaller weird number, 70, is not untouchable, since σ(134) − 134 = 70).

837 = 33 × 31. It is the 36th generalized heptagonal number.

838 = 2 × 419. It is a palindromic number. There are 838 distinct products ijk with 1 <= i<j<k <= 23.

839 is a prime number, a safe prime, a Chen prime, an Eisenstein prime with no imaginary part, and the sum of five consecutive primes (157 + 163 + 167 + 173 + 179). It is a highly cototient number.

840s

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, centered heptagonal number, centered octagonal number

842 = 2 × 421. It is a nontotient. There are 842 series-reduced trees with 18 nodes.

842!! - 1 is prime.

843 = 3 × 281. It is a Lucas number.

844 = 22 × 211. It is a nontotient. It is the smallest 5 consecutive integers which are not squarefree:

844 = 22 × 211, 845 = 5 × 132, 846 = 2 × 32 × 47, 847 = 7 × 112, and 848 = 24 × 53.

845 = 5 × 132. It is a concentric pentagonal number.There are 845 emergent parts in all partitions of 22.

846 = 2 × 32 × 47. It is a nontotient, a Harshad number, and the sum of eight consecutive primes (89 + 97 + 101 + 103 + 107 + 109 + 113 + 127).

847 = 7 × 112. It is a happy number. There are 847 partitions of 29 that do not contain 1 as a part.

848 = 24 × 53. It is an untouchable number.

849 = 3 × 283, It is a zero of Mertens function and a Blum integer.

850s

850 = 2 × 52 × 17. It is a zero of Mertens function and a nontotient. The sum of the squares of the divisors of 26 is 850 (sequence A001157 in the OEIS).

The maximum possible Fair Isaac credit score is 850.

851 = 23 × 37 There are 851 compositions of 18 into distinct parts

852 = 22 × 3 × 71. It is a pentagonal number and a Smith number.

853 is a prime number, a Perrin number, a zero of Mertens function, and a strictly non-palindromic number. The average of first 853 prime numbers is an integer (sequence A045345 in the OEIS). There are 853 connected graphs with 7 nodes.

854 = 2 × 7 × 61. It is a sphenic number and a nontotient. There are 854 unlabeled planar trees with 11 nodes.

855 = 32 × 5 × 19. It is a decagonal number and a centered cube number.

856 = 23 × 107. It is a nonagonal number, a centered pentagonal number, and a refactorable number.

857 is a prime number, a Chen prime, an Eisenstein prime with no imaginary part, and the sum of three consecutive primes (281 + 283 + 293).

858 = 2 × 3 × 11 × 13. It is a Giuga number.

859 is a prime number and a prime index prime. There are 859 planar partitions of 11.

860s

860 = 22 × 5 × 43. It is aHoax number and the sum of four consecutive primes (199 + 211 + 223 + 227).

861 = 3 × 7 × 41. It is a sphenic number, a hexagonal number, a Smith number, and the 41st triangular number.

862 = 2 × 431. It is a lazy caterer number.

863 is a prime number, a safe prime, a Chen prime, an Eisenstein prime with no imaginary part, and an index of a prime Lucas number.It is the sum of five consecutive primes (163 + 167 + 173 + 179 + 181) and the sum of seven consecutive primes (107 + 109 + 113 + 127 + 131 + 137 + 139).

864 = 25 × 33. It is an Achilles number and a Harshad number. It the sum of a twin prime pair (431 + 433) and the sum of six consecutive primes (131 + 137 + 139 + 149 + 151 + 157).

865 = 5 × 173.

866 = 2 × 433. It is a nontotient and the number of cubes of edge length 1 required to make a hollow cube of edge length 13. There are 866 one-sided noniamonds.

867 = 3 × 172. There are 867 5-chromatic simple graphs on 8 nodes.

868 = 22 × 7 × 31 = J3(10). It is a nontotient.

869 = 11 × 79. It is a zero of Mertens function.

870s

870 = 2 × 3 × 5 × 29. It is a pronic number, a nontotient, a sparsely totient number, a Harshad number, and the sum of ten consecutive primes (67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107). It is the magic constant of n×n normal magic square and n-queens problem for n = 12.

871 = 13 × 67. It is the thirteenth tridecagonal number.

872 = 23 × 109. It is a refactorable number and anontotient.

872! + 1 is prime.

873 = 32 × 97 = 1! + 2! + 3! + 4! + 5! + 6!.

874 = 2 × 19 × 23 = 0! + 1! + 2! + 3! + 4! + 5! + 6!. It is a sphenic number, a nontotient, a Harshad number, a happy number, and the sum of the first twenty-three primes.

875 = 53 × 7. It can be uniquely expressed as a difference of two positive cubes: 875 = 103 – 53.

876 = 22 × 3 × 73. It is a generalized pentagonal number.

877 is a prime number, a prime index prime, a Chen prime, a zero of Mertens function, a Bell number, and a strictly non-palindromic number.

878 = 2 × 439. It is a nontotient. There are 878 Pythagorean triples with a hypotenuse less than 1000.

879 = 3 × 293. It is a candidate Lychrel seed number. There are 879 regular hypergraphs spanning 4 vertices.

880s

880 = 24 × 5 × 11 = 11!!!. It is a Harshad number and a 148-gonal number. There are 880 n×n magic squares for n = 4.

881 is a prime number, a twin prime, a Chen prime, an Eisenstein prime with no imaginary part, and the sum of nine consecutive primes (79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113). It is a happy number.

881 is a bilingual play on words when text chatting in Mandarin Chinese or bilingually Mandarin Chinese and English. "881" is pronounced ba ba yi in Mandarin, and thus puns on "bye-bye." Probably an elaboration of the similar pun on "88" (ba-ba). See 88 (number).

882 = 2 × 32 × 72 =

(

9

5

)

2

{\displaystyle {\binom {9}{5}}_{2}}

It is a trinomial coefficient, a Harshad number, and the totient sum of the first 53 integers.

883 is a prime number, a twin prime, a lucky prime, the sum of three consecutive primes (283 + 293 + 307), and the sum of eleven consecutive primes (59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103). It is a zero of Mertens function.

884 = 22 × 13 × 17. It is a zero of Mertens function. There are 884 points on surface of tetrahedron with sidelength 21.

885 = 3 × 5 × 59. It is a sphenic number. There are 885 series-reduced rooted trees whose leaves are integer partitions whose multiset union is an integer partition of 7.

886 = 2 × 443. It is a zero of Mertens function.

890s

890 = 2 × 5 × 89. It is a sphenic number, a nontotient, and the sum of four consecutive primes (211 + 223 + 227 + 229). 890 is the sum of the squares of two successive primes: 890 = 192 + 232.

891 = 34 × 11. It is an octahedral number and the sum of five consecutive primes (167 + 173 + 179 + 181 + 191).

892 = 22 × 223. It is a nontotient. There are 892 regions formed by drawing the line segments connecting any two perimeter points of a 6 times 2 grid of squares like this (sequence A331452 in the OEIS).

893 = 19 × 47. It is a zero of Mertens function.

893 is considered an unlucky number in Japan, because its digits read sequentially are the literal translation of yakuza.

894 = 2 × 3 × 149. It is a sphenic number and a nontotient.

895 = 5 × 179. It is a Smith number, a Woodall number, and a zero of Mertens function.

896 = 27 × 7. It is a refactorable number, a zero of Mertens function, and the sum of six consecutive primes (137 + 139 + 149 + 151 + 157 + 163).

897 = 3 × 13 × 23. It is a sphenic number and a Cullen number (sequence A002064 in the OEIS).

898 = 2 × 449. It is a nontotient and a zero of Mertens function.

899 = 29 × 31. It is the product of a pair of twin primes, a happy number, and the smallest number with digit sum 26. There are 899 partitions of 51 into prime parts.