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

Author

Labos Elemer

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

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

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