A281904 Expansion of Sum_{i>=1} mu(i)^2*i*x^i/(1 - x^i) / Product_{j>=1} (1 - x^j), where mu() is the Moebius function (A008683).

1, 4, 9, 16, 31, 58, 93, 144, 221, 343, 502, 733, 1048, 1495, 2089, 2881, 3947, 5357, 7205, 9618, 12758, 16812, 22001, 28623, 37037, 47720, 61121, 77973, 99029, 125322, 157874, 198205, 247954, 309203, 384260, 476116, 588149, 724613, 890175, 1090781, 1333193, 1625702, 1977505, 2400221, 2906800, 3513121

Offset

1,2

Comments

Total sum of squarefree parts in all partitions of n.

Convolution of the sequences A000041 and A048250.

Links

Table of n, a(n) for n=1..46.

Index entries for related partition-counting sequences

Formula

G.f.: Sum_{i>=1} mu(i)^2*i*x^i/(1 - x^i) / Product_{j>=1} (1 - x^j).

Example

a(4) = 16 because we have [4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1] and 3 + 1 + 2 + 2 + 2 + 1 + 1 + 1 + 1 + 1 + 1 = 16.

Mathematica

nmax = 46; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 i x^i/(1 - x^i), {i, 1, nmax}] / Product[1 - x^j, {j, 1, nmax}], {x, 0, nmax}], x]]

Crossrefs

Cf. A000041, A005117, A008683, A048250, A066186, A073118.

Sequence in context: A138992 A199936 A326958 * A007679 A239870 A068037

Adjacent sequences: A281901 A281902 A281903 * A281905 A281906 A281907

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 01 2017

Status

approved