

A056675


Number of nonunitary but squarefree divisors of n!. Also number of unitary but notsquarefree divisors of n!.


1



0, 0, 0, 2, 4, 6, 12, 12, 12, 14, 28, 28, 56, 60, 60, 60, 120, 120, 240, 240, 240, 248, 496, 496, 496, 504, 504, 504, 1008, 1008, 2016, 2016, 2016, 2032, 2032, 2032, 4064, 4080, 4080, 4080, 8160, 8160, 16320, 16320, 16320, 16352, 32704, 32704, 32704, 32704
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OFFSET

1,4


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = A048656  A000005(A055231(n!)) = A048656  A000005(A007913(n!)/A055229(n!)).
a(n) = A056674(A000142(n)).  Amiram Eldar, Aug 06 2019


EXAMPLE

n=10: 10! = 2*2*2*2*2*2*2*2*3*3*3*3*5*5*7 = 256*81*25*7, which has 270 divisors, of which 16 are unitary and 16 are squarefree; overlap={1,7}. The set {2, 3, 5, 6, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210} represents the squarefree nonunitary divisors of 10!, so a(10)=14.


PROG

(PARI) a(n) = my(f=n!); sumdiv(f, d, issquarefree(d) && (gcd(d, f/d) != 1)); \\ Michel Marcus, Sep 05 2017


CROSSREFS

Cf. A000005, A000142, A007913, A048656, A055229, A055231, A056674.
Sequence in context: A182235 A180304 A053146 * A062857 A061799 A076868
Adjacent sequences: A056672 A056673 A056674 * A056676 A056677 A056678


KEYWORD

nonn


AUTHOR

Labos Elemer, Aug 10 2000


STATUS

approved



