Number of the day: 13120

Properties of the number 13120:

13120 = 2⁶ × 5 × 41 is the 11559^th composite number and is not squarefree.
13120 has 3 distinct prime factors, 28 divisors, 7 antidivisors and 5120 totatives.
13120 has a prime digit sum 7 in base 10.
13120 is the difference of 2 nonnegative squares in 10 ways.
13120 is the difference of 2 positive pentagonal numbers in 1 way.
13120 = 48² + 104² = 24² + 112² is the sum of 2 positive squares in 2 ways.
13120 = 40² + 48² + 96² is the sum of 3 positive squares.
13120² = 5376² + 11968² = 2880² + 12800² = 8512² + 9984² = 7872² + 10496² is the sum of 2 positive squares in 4 ways.
13120² is the sum of 3 positive squares.
13120 is a proper divisor of 337⁴ - 1.
13120 is palindromic in (at least) the following bases: 3, 25, 28, and -38.
13120 in base 3 = 122222221 and consists of only the digits '1' and '2'.
13120 in base 5 = 404440 and consists of only the digits '0' and '4'.
13120 in base 25 = kok and consists of only the digits 'k' and 'o'.
13120 in base 28 = gkg and consists of only the digits 'g' and 'k'.
13120 in base 34 = bbu and consists of only the digits 'b' and 'u'.
13120 in base 40 = 880 and consists of only the digits '0' and '8'.

The number 13120 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000141: Number of ways of writing n as a sum of 6 squares.
A006503: a(n) = n*(n+1)*(n+8)/6.
A006885: Record highest point of trajectory before reaching 1 in `3x+1' problem, corresponding to starting values in A006884.
A035008: Total number of possible knight moves on an (n+2) X (n+2) chessboard, if the knight is placed anywhere.
A077635: LCM of terms in periodic part of continued fraction expansion of square root of -1+3^n.
A087701: Maximal term in Collatz-iteration started at -1+2^n.
A100774: a(n) = 2*(3^n - 1).
A137491: Numbers with 28 divisors.
A164123: Partial sums of A162436.
A179672: Products of the 6st power of a prime and 2 distinct primes (p^6*q*r).