Number of the day: 7560

Properties of the number 7560:

7560 = 2³ × 3³ × 5 × 7 is the 6600^th composite number and is not squarefree.
7560 has 4 distinct prime factors, 64 divisors, 17 antidivisors and 1728 totatives.
7560 = 18³ + 12³ is the sum of 2 positive cubes in 1 way.
7560 is the difference of 2 nonnegative squares in 16 ways.
7560 is the sum of 2 positive triangular numbers.
7560 is the difference of 2 positive pentagonal numbers in 1 way.
7560 = 8² + 10² + 86² is the sum of 3 positive squares.
7560² = 4536² + 6048² is the sum of 2 positive squares in 1 way.
7560² is the sum of 3 positive squares.
7560 is a proper divisor of 379² - 1.
7560 = '756' + '0' is the concatenation of 2 oblong numbers.
7560 is palindromic in (at least) the following bases: 89, and -32.
7560 in base 3 = 101101000 and consists of only the digits '0' and '1'.
7560 in base 5 = 220220 and consists of only the digits '0' and '2'.
7560 in base 6 = 55000 and consists of only the digits '0' and '5'.
7560 in base 19 = 11hh and consists of only the digits '1' and 'h'.
7560 in base 20 = ii0 and consists of only the digits '0' and 'i'.
7560 in base 27 = aa0 and consists of only the digits '0' and 'a'.
7560 in base 35 = 660 and consists of only the digits '0' and '6'.

The number 7560 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002182: Highly composite numbers, definition (1): where d(n), the number of divisors of n (A000005), increases to a record.
A003680: Smallest number with 2n divisors.
A007416: The minimal numbers: sequence A005179 arranged in increasing order.
A049598: 12 times triangular numbers.
A067128: Ramanujan's largely composite numbers, defined to be numbers n such that d(n) >= d(k) for k = 1 to n-1.
A104350: Partial products of largest prime factors of numbers <= n.
A157400: A partition product with biggest-part statistic of Stirling_1 type (with parameter k = -2) as well as of Stirling_2 type (with parameter k = -2), (triangle read by rows).
A171701: The first n-fold (at least) intrinsically 2-palindromic number (in base ten)
A245334: A factorial-like triangle read by rows: T(0,0) = 1; T(n+1,0) = T(n,0)+1; T(n+1,k+1) = T(n,0)*T(n,k), k=0..n.
A256634: Numbers n such that the decimal expansions of both n and n^2 have 0 as smallest digit and 7 as largest digit.