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

1,3

Links

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

Formula

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

a(n) = A027423(n) - A055993(n). - Amiram Eldar, 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 *)

Prog

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

Crossrefs

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

Sequence in context: A291987 A200823 A093866 * A026341 A026271 A166212

Adjacent sequences: A056593 A056594 A056595 * A056597 A056598 A056599

Keyword

nonn

Author

Labos Elemer, Jul 21 2000

Status

approved