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 A286872 a(n) is the number of terms m such that d((m!)^n) (mod d(m!)) == 0, where d is A000005. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS a(1) equals infinity. LINKS Robert G. Wilson v, Table of n, a(n) for n = 2..1252 FORMULA a(2n) = 1. a(2n+1) = A286835(n). 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] CROSSREFS Cf. A286835. Sequence in context: A222182 A126155 A021197 * A073116 A201525 A269229 Adjacent sequences:  A286869 A286870 A286871 * A286873 A286874 A286875 KEYWORD nonn AUTHOR Robert G. Wilson v, Aug 02 2017 STATUS approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)