A284829 Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) * Product_{j>=i} 1/(1 - mu(j)^2*x^j), where mu() is the Moebius function (A008683).

1, 3, 5, 9, 13, 23, 30, 45, 64, 89, 118, 165, 211, 282, 369, 475, 606, 779, 978, 1236, 1547, 1922, 2375, 2936, 3602, 4403, 5362, 6506, 7864, 9493, 11399, 13661, 16317, 19443, 23122, 27415, 32418, 38268, 45065, 52968, 62125, 72742, 84969, 99112, 115409, 134139, 155665, 180368, 208658, 241051

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..50.

Index entries for related partition-counting sequences

Formula

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

Example

a(5) = 13 because we have [5], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 1 + 1 + 2 + 1 + 3 + 5 = 13.

Mathematica

nmax = 50; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i/(1 - x^i) Product[1/(1 - MoebiusMu[j]^2 x^j), {j, i, nmax}], {i, 1, nmax}], {x, 0, nmax}], x]]

Prog

(PARI) x='x+O('x^50); Vec(sum(i=1, 50, moebius(i)^2*x^i/(1 - x^i) * prod(j=i, 50, 1/(1 - moebius(j)^2*x^j)))) \\ Indranil Ghosh, Apr 04 2017

Crossrefs

Cf. A005117, A008683, A073576, A092268, A092269, A195820, A281572.

Sequence in context: A146905 A052282 A001993 * A153263 A295140 A144933

Adjacent sequences: A284826 A284827 A284828 * A284830 A284831 A284832

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2017

Status

approved