Number of the day: 5300

Properties of the number 5300:

5300 = 2² × 5² × 53 is the 4597^th composite number and is not squarefree.
5300 has 3 distinct prime factors, 18 divisors, 7 antidivisors and 2080 totatives.
5300 has a Fibonacci digit sum 8 in base 10.
5300 = 8³ + … + 12³ is the sum of at least 2 consecutive cubes.
5300 = (39 × 40)/2 + … + (44 × 45)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
5300 = 1326² - 1324² = 270² - 260² = 78² - 28² is the difference of 2 nonnegative squares in 3 ways.
5300 is the difference of 2 positive pentagonal numbers in 3 ways.
5300 = 44² + 58² = 26² + 68² = 20² + 70² is the sum of 2 positive squares in 3 ways.
5300 = 4² + 10² + 72² is the sum of 3 positive squares.
5300² = 3180² + 4240² = 1920² + 4940² = 460² + 5280² = 2800² + 4500² = 3536² + 3948² = 1484² + 5088² = 1428² + 5104² is the sum of 2 positive squares in 7 ways.
5300² is the sum of 3 positive squares.
5300 is a proper divisor of 1801² - 1.
5300 is palindromic in (at least) the following bases: 23, 99, -23, and -27.
5300 in base 22 = akk and consists of only the digits 'a' and 'k'.
5300 in base 23 = a0a and consists of only the digits '0' and 'a'.
5300 in base 27 = 778 and consists of only the digits '7' and '8'.
5300 in base 32 = 55k and consists of only the digits '5' and 'k'.

The number 5300 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A091004: Expansion of x(1-x)/((1-2x)(1+3x)).
A091150: Triangle, read by rows, where the n-th row lists the coefficients of the polynomial of degree n that generates the n-th diagonal of this sequence.
A091151: Row sums of triangle A091150, in which the n-th row lists the coefficients of the polynomial of degree n that generates the n-th diagonal.
A152135: Maximal length of rook tour on an n X n+4 board.
A192476: Monotonic ordering of set S generated by these rules: if x and y are in S then x^2 + y^2 is in S, and 1 is in S.
A195805: T(n,k)=Number of triangular nXnXn 0..k arrays with all rows and diagonals having the same length having the same sum, with corners zero
A200192: T(n,k)=Number of -k..k arrays x(0..n-1) of n elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing
A224652: Triangle read by rows: T(n,k) is the number of permutations of n elements with k the (smallest) header (first element) of the longest descending subsequence.
A249960: T(n,k)=Number of length n+5 0..k arrays with no six consecutive terms having the maximum of any two terms equal to the minimum of the remaining four terms
A252192: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 1 3 6 or 7 and every 3X3 diagonal and antidiagonal sum not equal to 0 1 3 6 or 7