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%I #15 Aug 07 2017 21:26:54
%S 1,5,1,8,1,15,1,6,1,29,1,27,1,5,1,54,1,60,1,6,1,63,1,7,1,6,1,54,1,75,
%T 1,6,1,12,1,52,1,7,1,76,1,69,1,5,1,74,1,27,1,6,1,78,1,12,1,6,1,97,1,
%U 33,1,6,1,15,1,85,1,5,1,99,1,46,1,5,1,15,1,95,1,6,1,56,1,13,1,6,1,82,1,20,1,5
%N a(n) is the number of terms m such that d((m!)^n) (mod d(m!)) == 0, where d is A000005.
%C a(1) equals infinity.
%H Robert G. Wilson v, <a href="/A286872/b286872.txt">Table of n, a(n) for n = 2..1252</a>
%F a(2n) = 1. a(2n+1) = A286835(n).
%t factExpLst[nbr_] := factExpLst[nbr] = Table[Plus @@ Rest@ NestWhileList[ Floor[#/prm] &, nbr, # > 0 &], {prm, Prime@ Range@ PrimePi@ nbr}] (* which is the same as Transpose[ FactorInteger[ nbr!]][[2]] *); ds0[nbr_, exp_] := Times @@ (1 + exp*factExpLst[ nbr]); fQ[nbr_, exp_] := Mod[ds0[nbr, exp], ds0[nbr, 1]] == 0; f[n_] := f[n] = If[EvenQ@ n, {1}, Select[Range@ 100000, fQ[#, n] &]]; f[1] = {}; Array[ Length@ f@# &, 70]
%Y Cf. A286835.
%K nonn
%O 2,2
%A _Robert G. Wilson v_, Aug 02 2017
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