|
|
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
|
|
|
FORMULA
|
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|