A308492 Expansion of Sum_{i>=1} mu(i) * x^i * Product_{j>=1} (1 - x^(i*j))^24.

1, -25, 251, -1448, 4829, -6275, -16745, 85952, -113895, -120725, 534611, -363448, -577739, 418625, 1212079, 902656, -6905935, 2847375, 10661419, -6992392, -4202995, -13365275, 18643271, 21573952, -25504055, 14443475, -73165437, 24246760, 128406629, -30301975

Offset

1,2

Comments

Moebius transform of A000594.

Links

Table of n, a(n) for n=1..30.

Eric Weisstein's World of Mathematics, Tau Function

Formula

a(n) = Sum_{d|n} mu(n/d)*A000594(d).

Example

G.f. = x - 25*x^2 + 251*x^3 - 1448*x^4 + 4829*x^5 - 6275*x^6 - 16745*x^7 + 85952*x^8 - 113895*x^9 - 120725*x^10 + ...

Mathematica

nmax = 30; CoefficientList[Series[Sum[MoebiusMu[i] x^i Product[(1 - x^(i j))^24, {j, 1, nmax}], {i, 1, nmax}], {x, 0, nmax}], x] // Rest
a[n_] := Sum[MoebiusMu[n/d] RamanujanTau[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 30}]

Prog

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*ramanujantau(d)); \\ Michel Marcus, Jun 01 2019

Crossrefs

Cf. A000594, A008683, A034777, A034778.

Sequence in context: A126546 A023073 A022685 * A042208 A143009 A090022

Adjacent sequences: A308489 A308490 A308491 * A308493 A308494 A308495

Keyword

sign,mult

Author

Ilya Gutkovskiy, May 31 2019

Status

approved