A281667 Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 + x^i) * Product_{j>=1} (1 + mu(j)^2*x^j), where mu() is the Moebius function (A008683).

1, 1, 3, 2, 3, 6, 5, 9, 10, 12, 15, 16, 20, 24, 27, 38, 41, 48, 56, 62, 78, 88, 101, 120, 131, 149, 174, 189, 221, 243, 278, 318, 349, 394, 444, 491, 556, 622, 693, 773, 849, 953, 1048, 1158, 1292, 1422, 1568, 1735, 1901, 2101, 2307, 2534, 2795, 3060, 3357, 3681, 4024, 4404, 4809, 5245, 5734, 6242, 6805, 7418

Offset

1,3

Comments

Total number of parts in all partitions of n into distinct squarefree parts (A005117).

Links

Table of n, a(n) for n=1..64.

Index entries for related partition-counting sequences

Formula

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

Example

a(8) = 9 because we have [7, 1], [6, 2], [5, 3], [5, 2, 1] and 2 + 2 + 2 + 3 = 9.

Mathematica

nmax = 64; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i/(1 + x^i), {i, 1, nmax}] Product[1 + MoebiusMu[j]^2 x^j, {j, 1, nmax}], {x, 0, nmax}], x]]

Crossrefs

Cf. A005117, A008683, A015723, A024938, A087188, A281572.

Sequence in context: A033807 A371070 A058691 * A368102 A336749 A214297

Adjacent sequences: A281664 A281665 A281666 * A281668 A281669 A281670

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 26 2017

Status

approved