### Properties of the number 53952:

53952 = 2^{6}× 3 × 281 is the 48454

^{th}composite number and is not squarefree.

53952 has 3 distinct prime factors, 28 divisors, 9 antidivisors and 17920 totatives.

53952 is the difference of 2 nonnegative squares in 10 ways.

53952 = 56

^{2}+ 104

^{2}+ 200

^{2}is the sum of 3 positive squares.

53952

^{2}= 30720

^{2}+ 44352

^{2}is the sum of 2 positive squares in 1 way.

53952

^{2}is the sum of 3 positive squares.

53952 is a divisor of 89

^{8}- 1.

53952 is palindromic in (at least) base -43.

53952 in base 3 = 2202000020 and consists of only the digits '0' and '2'.

53952 in base 42 = UOO and consists of only the digits 'O' and 'U'.

### The number 53952 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.A080877: a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=2.

A080878: a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=3.

A098648: Expansion of (1-3*x)/(1 - 6*x + 4*x^2).

A149377: Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (-1, 0, 1), (1, -1, 0), (1, 1, -1), (1, 1, 0)}

A205071: Number of (n+1)X8 0..1 arrays with the number of rightwards and downwards edge increases in each 2X2 subblock differing from the number in all its horizontal and vertical neighbors

A234645: Sum of the divisors of n^3+1.

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