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Number of non-unitary divisors of n!.
5

%I #14 Jul 09 2019 10:57:31

%S 0,0,0,4,8,22,44,80,144,254,508,760,1520,2528,3968,5312,10624,14560,

%T 29120,40784,60544,95744,191488,242368,339520,531712,676864,916768,

%U 1833536,2331776,4663552,5527552,7862272,12163072,16420864,19593472

%N Number of non-unitary divisors of n!.

%H Amiram Eldar, <a href="/A048657/b048657.txt">Table of n, a(n) for n = 1..1000</a>

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

%F a(n) = A048105(n!). - _Michel Marcus_, Jun 30 2017

%e 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.

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

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

%K nonn

%O 1,4

%A _Labos Elemer_