A284835 Expansion of Sum_{i>=1} mu(i)^2*x^i/(1 - x^i) * Product_{j=1..i} 1/(1 - mu(j)^2*x^j), where mu() is the Moebius function (A008683).

1, 3, 5, 8, 11, 18, 22, 31, 39, 53, 64, 87, 104, 134, 165, 205, 248, 310, 368, 455, 545, 659, 784, 947, 1117, 1337, 1579, 1872, 2197, 2604, 3036, 3570, 4168, 4866, 5661, 6599, 7633, 8859, 10236, 11831, 13625, 15715, 18036, 20728, 23761, 27211, 31106, 35560, 40533, 46221, 52596, 59813, 67912, 77090, 87343

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..55.

Index entries for related partition-counting sequences

Formula

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

Example

a(5) = 11 because we have [5], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 1 + 1 + 1 + 2 + 1 + 5 = 11.

Mathematica

nmax = 55; Rest[CoefficientList[Series[Sum[MoebiusMu[i]^2 x^i/(1 - x^i) Product[1/(1 - MoebiusMu[j]^2 x^j), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]]

Prog

(PARI) x='x+O('x^56); Vec(sum(i=1, 56, moebius(i)^2*x^i/(1 - x^i) * prod(j=1, i, 1/(1 - moebius(j)^2*x^j)))) \\ Indranil Ghosh, Apr 04 2017

Crossrefs

Cf. A005117, A008683, A046746, A073576, A092311, A281572, A284829.

Sequence in context: A338204 A244031 A194803 * A308266 A320594 A227563

Adjacent sequences: A284832 A284833 A284834 * A284836 A284837 A284838

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2017

Status

approved