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A055993
Number of square divisors of n!.
8
1, 1, 1, 2, 2, 6, 6, 8, 12, 30, 30, 36, 36, 72, 96, 128, 128, 180, 180, 300, 300, 600, 600, 864, 1152, 2304, 2688, 4368, 4368, 5376, 5376, 6144, 6144, 13056, 16320, 19440, 19440, 38880, 43200, 48000, 48000, 64000, 64000, 100800, 133056, 278784, 278784
OFFSET
1,4
LINKS
FORMULA
a(n) = A046951(n!) = A000005(A055772(n)) = A000005(A000188(A000142(n))).
MATHEMATICA
Table[Count[Divisors[n!], d_ /; IntegerQ@ Sqrt@ d], {n, 30}] (* Michael De Vlieger, Feb 05 2017 *)
PROG
(PARI) a(n) = sumdiv(n!, d, issquare(d)); \\ Michel Marcus, Dec 26 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 21 2000
STATUS
approved