Number of the day: 5085

Properties of the number 5085:

5085 = 3² × 5 × 113 is the 4405^th composite number and is not squarefree.
5085 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 2688 totatives.
5085 = 2543² - 2542² = 849² - 846² = 511² - 506² = 287² - 278² = 177² - 162² = 79² - 34² is the difference of 2 nonnegative squares in 6 ways.
5085 is the sum of 2 positive triangular numbers.
5085 is the difference of 2 positive pentagonal numbers in 1 way.
5085 = 27² + 66² = 18² + 69² is the sum of 2 positive squares in 2 ways.
5085 = 10² + 19² + 68² is the sum of 3 positive squares.
5085² = 2484² + 4437² = 675² + 5040² = 3564² + 3627² = 3051² + 4068² is the sum of 2 positive squares in 4 ways.
5085² is the sum of 3 positive squares.
5085 is a proper divisor of 467⁴ - 1.
5085 is palindromic in (at least) the following bases: 62, -42, and -82.
5085 in base 21 = bb3 and consists of only the digits '3' and 'b'.
5085 in base 41 = 311 and consists of only the digits '1' and '3'.
5085 in base 61 = 1MM and consists of only the digits '1' and 'M'.
5085 in base 62 = 1K1 and consists of only the digits '1' and 'K'.

The number 5085 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A024794: Number of 10's in all partitions of n.
A056108: Fourth spoke of a hexagonal spiral.
A067563: Product of n-th prime number and n-th composite number.
A100980: Number of totally ramified extensions over Q_3 with degree n in the algebraic closure of Q_3.
A137962: G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^5)^3.
A180906: T(n,k)=number of sequences of n integers p(i) i=0..n-1 0<=p(i)<=k*i and |p(i+1)-p(i)|<=k
A205644: Nonnegative values x of solutions (x, y) to the Diophantine equation x^2+(x+287)^2 = y^2.
A211013: Second 13-gonal numbers: a(n) = n*(11*n+9)/2.
A231688: a(n) = Sum_{i=0..n} digsum(i)^3, where digsum(i) = A007953(i).
A252075: T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock row, column, diagonal and antidiagonal sum not equal to 0 3 or 4