

A056596


Number of nonsquare divisors of n!.


1



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
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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



