Monday, November 28, 2016

Number of the day: 5800

Properties of the number 5800:

5800 = 23 × 52 × 29 is the 5039th composite number and is not squarefree.
5800 has 3 distinct prime factors, 24 divisors, 11 antidivisors and 2240 totatives.
5800 has an emirp digit sum 13 in base 10.
5800 has a Fibonacci digit sum 13 in base 10.
5800 = 14512 - 14492 = 7272 - 7232 = 2952 - 2852 = 1552 - 1352 = 832 - 332 = 792 - 212 is the difference of 2 nonnegative squares in 6 ways.
5800 is the sum of 2 positive triangular numbers.
5800 is the difference of 2 positive pentagonal numbers in 3 ways.
5800 = 302 + 702 = 382 + 662 = 182 + 742 is the sum of 2 positive squares in 3 ways.
5800 = 302 + 422 + 562 is the sum of 3 positive squares.
58002 = 34802 + 46402 = 9602 + 57202 = 6802 + 57602 = 40002 + 42002 = 29122 + 50162 = 16242 + 55682 = 26642 + 51522 is the sum of 2 positive squares in 7 ways.
58002 is the sum of 3 positive squares.
5800 is a divisor of 3492 - 1.
5800 is palindromic in (at least) the following bases: 36, 99, and -42.
5800 in base 3 = 21221211 and consists of only the digits '1' and '2'.
5800 in base 12 = 3434 and consists of only the digits '3' and '4'.
5800 in base 17 = 1313 and consists of only the digits '1' and '3'.
5800 in base 35 = 4pp and consists of only the digits '4' and 'p'.
5800 in base 36 = 4h4 and consists of only the digits '4' and 'h'.

The number 5800 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A026054: dot_product(n,n-1,...2,1).(3,4,...,n,1,2).
A060488: Number of 4-block ordered tricoverings of an unlabeled n-set.
A082227: Main diagonal of array A082224.
A138992: a(n) = Frobenius number for 6 successive primes = F[p(n),p(n+1),p(n+2),p(n+3),p(n+4),p(n+5)].
A164770: Numbers n with property that average digit of n^2 is 2.
A184071: T(n,k)=Number of (n+1)X(k+1) binary arrays with rows and columns in nondecreasing order and with no 2X2 subblock sum differing from a horizontal or vertical neighbor subblock sum by more than one
A211971: Column 0 of square array A211970 (in which column 1 is A000041).
A216046: Expansion of (chi(-x) / chi^3(-x^3))^2 in powers of x where chi() is a Ramanujan theta function.
A241343: Number of partitions p of n such that neither floor(mean(p)) nor ceiling(mean(p)) is a part.
A241515: Number of partitions of n such that (number parts having multiplicity 1) is a part or (number of parts > 1) is a part.

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