A344268 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^(5^(k-1)).

1, 5, 25, 135, 625, 3250, 15625, 78760, 390925, 1956250, 9765625, 48847125, 244140625, 1220781250, 6103531250, 30517977755, 152587890625, 762941485875, 3814697265625, 19073496178125, 95367432031250, 476837207031250, 2384185791015625, 11920929201609625, 59604644775585625, 298023225097656250

Offset

1,2

Links

Table of n, a(n) for n=1..26.

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)^(5^(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, 26] (* after Jean-François Alcover in A007896 *)

Crossrefs

Cf. A045778, A050368, A344249, A344265, A344266, A344267, A344269, A344270, A344271.

Sequence in context: A351587 A225963 A222570 * A144818 A366431 A048370

Adjacent sequences: A344265 A344266 A344267 * A344269 A344270 A344271

Keyword

nonn

Author

Ilya Gutkovskiy, May 13 2021

Status

approved