OFFSET
1,2
COMMENTS
Moebius transform of A000594.
LINKS
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
KEYWORD
sign,mult
AUTHOR
Ilya Gutkovskiy, May 31 2019
STATUS
approved