A344298 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(9^(k-1)).

1, 9, 81, 765, 6561, 59778, 531441, 4789614, 43049961, 387479538, 3486784401, 31381653015, 282429536481, 2541870611298, 22876792986402, 205891175433096, 1853020188851841, 16677182091899187, 150094635296999121, 1350851721164795655, 12157665459099975522, 109418989162893418818

Offset: 1

Author

Ilya Gutkovskiy, May 14 2021

Keywords

• nonn

Crossrefs

Cf. A045778, A050368, A344253, A344265, A344266, A344267, A344268, A344269, A344270, A344271.

Programs

Mathematica

dircon[v_, w_] := Module[{lv = Length[v], lw = Length[w], fv, fw}, fv[n_] := If[n <= lv, v[[n]], 0]; fw[n_] := If[n <= lw, w[[n]], 0]; Table[ DirichletConvolve[fv[n], fw[n], n, m], {m, Min[lv, lw]}]];
a[n_] := Module[{A, v, w, m}, If[n<1, 0, v = Table[Boole[k == 1], {k, n}]; For[k = 2, k <= n, k++, m = Length[IntegerDigits[n, k]] - 1; A = (1 + x)^(9^(k - 1)) + x*O[x]^m // Normal; w = Table[0, {n}]; For[i = 0, i <= m, i++, w[[k^i]] = Coefficient[A, x, i]]; v = dircon[v, w]]; v[[n]]]];
Array[a, 22] (* after Jean-François Alcover in A007896 *)