A286872 a(n) is the number of terms m such that d((m!)^n) (mod d(m!)) == 0, where d is A000005.

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, 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, 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

Offset: 2

Author

Robert G. Wilson v, Aug 02 2017

Keywords

• nonn

Comments

a(1) equals infinity.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 2..1252

Crossrefs

Cf. A286835.

Programs

Mathematica

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]

Formula

a(2n) = 1. a(2n+1) = A286835(n).