OFFSET
0,3
FORMULA
G.f.: Product_{p prime, k>=1} 1 / (1 - x^(p^k-1)).
MATHEMATICA
nmax = 48; CoefficientList[Series[Product[1/(1 - Boole[PrimePowerQ[k + 1]] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d Boole[PrimePowerQ[d + 1]], {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 48}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 06 2021
STATUS
approved