A318025 Expansion of Sum_{k>=1} (-1 + Product_{j>=1} 1/(1 - j*x^(k*j))).

1, 4, 7, 18, 26, 66, 98, 216, 361, 701, 1171, 2287, 3763, 6887, 11707, 20740, 34637, 60678, 100581, 172609, 285924, 481671, 791317, 1323831, 2156856, 3561119, 5784021, 9459559, 15250217, 24783964, 39713789, 64032664, 102200203, 163617694, 259745174, 413886941, 653715969, 1035539948

Offset

1,2

Comments

Inverse Moebius transform of A006906.

Links

Table of n, a(n) for n=1..38.

N. J. A. Sloane, Transforms

Formula

G.f.: Sum_{k>=1} A006906(k)*x^k/(1 - x^k).

a(n) = Sum_{d|n} A006906(d).

Mathematica

nmax = 38; Rest[CoefficientList[Series[Sum[-1 + Product[1/(1 - j x^(k j)), {j, 1, nmax}], {k, 1, nmax}], {x, 0, nmax}], x]]
b[n_] := b[n] = SeriesCoefficient[Product[1/(1 - k x^k), {k, 1, n}], {x, 0, n}]; a[n_] := a[n] = SeriesCoefficient[Sum[b[k] x^k/(1 - x^k), {k, 1, n}], {x, 0, n}]; Table[a[n], {n, 38}]
Table[Sum[Total[Times @@@ IntegerPartitions[d]], {d, Divisors[n]}], {n, 38}]

Crossrefs

Cf. A006906, A047968, A300277, A302549, A318290.

Sequence in context: A080650 A276187 A357041 * A005509 A147366 A056318

Adjacent sequences: A318022 A318023 A318024 * A318026 A318027 A318028

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 23 2018

Status

approved