A048657 Number of non-unitary divisors of n!.

0, 0, 0, 4, 8, 22, 44, 80, 144, 254, 508, 760, 1520, 2528, 3968, 5312, 10624, 14560, 29120, 40784, 60544, 95744, 191488, 242368, 339520, 531712, 676864, 916768, 1833536, 2331776, 4663552, 5527552, 7862272, 12163072, 16420864, 19593472

Offset

1,4

Links

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

Formula

a(n) = A000005(n!) - 2^(A000720(n)).

a(n) = A048105(n!). - Michel Marcus, Jun 30 2017

Example

n=5, 5!=120 has 16 divisors of which 8 are not unitary:{2,60,4,30,6,20,10,12} while {1,120,3,40,5,24,15,16} are the unitary ones.

Mathematica

Table[Function[k, DivisorSum[k, 1 &, ! CoprimeQ[#, k/#] &]][n!], {n, 30}] (* Michael De Vlieger, Jun 29 2017 *)

Crossrefs

Cf. A000005, A000720, A027423, A034444, A048105, A048656.

Sequence in context: A200149 A153765 A003606 * A322284 A175655 A000639

Adjacent sequences: A048654 A048655 A048656 * A048658 A048659 A048660

Keyword

nonn

Author

Labos Elemer

Status

approved