A351402 G.f. A(x) satisfies: 1 / (1 - x) = Product_{i>=1, j>=1} A(x^(i*j)).

1, 1, -1, -3, -1, 1, 4, 2, -2, -5, 4, 2, -2, -10, 3, 10, 21, -15, -26, -23, 34, 28, 25, -54, -18, 2, 67, -48, -22, -55, 116, 44, 37, -227, -10, 32, 295, -85, -76, -336, 254, 74, 250, -451, 59, -127, 672, -294, -69, -761, 740, 77, 657, -1208, 59, -450, 1700, -487, 241, -1892, 1202

Offset

0,4

Comments

Euler transform of A007427.

Links

Table of n, a(n) for n=0..60.

Formula

G.f. A(x) satisfies: 1 / (1 - x) = Product_{k>=1} A(x^k)^A000005(k).

G.f.: Product_{k>=1} 1 / (1 - x^k)^A007427(k).

G.f.: exp( Sum_{k>=1} A101035(k) * x^k / k ).

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} A101035(k) * a(n-k).

Mathematica

nmax = 60; A007427[n_] := Sum[MoebiusMu[d] MoebiusMu[n/d], {d, Divisors[n]}]; CoefficientList[Series[Product[1/(1 - x^k)^A007427[k], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000005, A006171, A007427, A101035, A117209, A351403.

Sequence in context: A134557 A290342 A219842 * A134264 A125181 A157076

Adjacent sequences: A351399 A351400 A351401 * A351403 A351404 A351405

Keyword

sign

Author

Ilya Gutkovskiy, Feb 10 2022

Status

approved