A357524 Expansion of Product_{k>=1} 1 / (1 + mu(k)*x^k).

1, -1, 2, -1, 2, 0, 1, 2, 0, 3, 0, 4, 1, 4, 2, 4, 4, 4, 5, 6, 6, 6, 8, 8, 10, 9, 11, 12, 13, 14, 17, 17, 20, 19, 23, 24, 28, 27, 30, 34, 34, 40, 41, 47, 48, 50, 56, 62, 64, 71, 72, 80, 85, 91, 99, 104, 113, 112, 128, 135, 147, 153, 159, 176, 180, 196, 210, 220, 233, 240, 264

Offset

0,3

Links

Table of n, a(n) for n=0..70.

Mathematica

nmax = 70; CoefficientList[Series[Product[1/(1 + MoebiusMu[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = (1/n) Sum[Sum[d (-MoebiusMu[d])^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 70}]

Crossrefs

Cf. A008683, A117211, A185694, A300663, A306327, A329069, A357521, A357525.

Sequence in context: A135387 A321104 A127442 * A115628 A114002 A114004

Adjacent sequences: A357521 A357522 A357523 * A357525 A357526 A357527

Keyword

sign

Author

Ilya Gutkovskiy, Oct 02 2022

Status

approved