A328706 Dirichlet g.f.: Product_{k>=2} (1 + k^(-s))^2.

1, 2, 2, 3, 2, 6, 2, 6, 3, 6, 2, 12, 2, 6, 6, 9, 2, 12, 2, 12, 6, 6, 2, 24, 3, 6, 6, 12, 2, 22, 2, 14, 6, 6, 6, 28, 2, 6, 6, 24, 2, 22, 2, 12, 12, 6, 2, 42, 3, 12, 6, 12, 2, 24, 6, 24, 6, 6, 2, 52, 2, 6, 12, 22, 6, 22, 2, 12, 6, 22, 2, 60, 2, 6, 12, 12, 6, 22, 2, 42

Offset: 1

Author

Ilya Gutkovskiy, Oct 26 2019

Keywords

• nonn

Comments

Dirichlet convolution of A045778 with itself.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Jacob Sprittulla, On Colored Factorizations, arXiv:2008.09984 [math.CO], 2020.

Crossrefs

Cf. A045778, A301830.

Programs

Mathematica

Block[{f}, f[m_, 1] := 1; f[1, n_] := 0; f[1, 1] := 1; f[0, n_] := 0; f[m_, n_] := f[m, n] = Total[f[# - 1, n/#] & /@ Select[Divisors[n], # <= m &]]; Table[DivisorSum[n, f[n/#, n/#]*f[#, #] &], {n, 80}]] (* Michael De Vlieger, Nov 04 2020 *)

Formula

a(n) = Sum_{d|n} A045778(n/d) * A045778(d).