A056596 Number of nonsquare divisors of n!.

0, 1, 3, 6, 14, 24, 54, 88, 148, 240, 510, 756, 1548, 2520, 3936, 5248, 10624, 14508, 29196, 40740, 60500, 95400, 191400, 242016, 338880, 529920, 674688, 912912, 1830192, 2327424, 4660224, 5523456, 7858176, 12152064, 16406592, 19576080

Offset: 1

Author

Labos Elemer, Jul 21 2000

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

A000142, A000005, A046951, A055772, A027423, A055993.

Programs

Magma

[#[d:d in Divisors(Factorial(n))| not IsSquare(d)]:n in [1..36]]; // Marius A. Burtea, Jul 16 2019

Mathematica

Table[Count[Divisors[n!], d_ /; !IntegerQ@ Sqrt@ d], {n, 30}] (* Amiram Eldar, Jul 16 2019 after Michael De Vlieger at A055993 *)

Formula

a(n) = d(n!) - A046951(n!)

a(n) = A027423(n) - A055993(n). - Amiram Eldar, Jul 16 2019