A318845 a(n) = Sum_{d|n} (-1)^(n/d+1) * Sum_{j|d} sigma(j), where sigma(j) = sum of divisors of j (A000203).

1, 3, 6, 6, 8, 18, 10, 10, 24, 24, 14, 36, 16, 30, 48, 15, 20, 72, 22, 48, 60, 42, 26, 60, 46, 48, 82, 60, 32, 144, 34, 21, 84, 60, 80, 144, 40, 66, 96, 80, 44, 180, 46, 84, 192, 78, 50, 90, 76, 138, 120, 96, 56, 246, 112, 100, 132, 96, 62, 288, 64, 102, 240, 28, 128, 252, 70, 120, 156, 240

Offset

1,2

Links

Table of n, a(n) for n=1..70.

Formula

G.f.: Sum_{k>=1} A007429(k)*x^k/(1 + x^k).

L.g.f.: log(Product_{k>=1} (1 + x^k)^(A007429(k)/k)) = Sum_{n>=1} a(n)*x^n/n.

Mathematica

Table[Sum[(-1)^(n/d + 1) Sum[DivisorSigma[1, j], {j, Divisors[d]}], {d, Divisors[n]}], {n, 70}]
nmax = 70; Rest[CoefficientList[Series[Sum[DivisorSum[k, DivisorSigma[1, #] &] x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]
nmax = 70; Rest[CoefficientList[Series[Log[Product[(1 + x^k)^(DivisorSum[k, DivisorSigma[1, #] &]/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]

Crossrefs

Cf. A000203, A007429, A007430, A288417, A318768.

Sequence in context: A025500 A141218 A342425 * A147866 A135702 A108850

Adjacent sequences: A318842 A318843 A318844 * A318846 A318847 A318848

Keyword

nonn,mult

Author

Ilya Gutkovskiy, Sep 04 2018

Status

approved