A327960 Dirichlet g.f.: 1 / (zeta(s) * zeta(s-1)^2).

1, -5, -7, 8, -11, 35, -15, -4, 15, 55, -23, -56, -27, 75, 77, 0, -35, -75, -39, -88, 105, 115, -47, 28, 35, 135, -9, -120, -59, -385, -63, 0, 161, 175, 165, 120, -75, 195, 189, 44, -83, -525, -87, -184, -165, 235, -95, 0, 63, -175, 245, -216, -107, 45, 253, 60, 273, 295, -119, 616

Offset

1,2

Comments

Dirichlet inverse of A060640.

Moebius transform applied twice to A101035.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1; a(n) = -Sum_{d|n, d<n} A060640(n/d) * a(d).

a(n) = Sum_{d|n} A046692(n/d) * A055615(d).

Multiplicative with a(p^e) = -(2*p+1) if e=1, p^2+2*p if e=2, -p^2 if e=3, and 0 otherwise. - Amiram Eldar, Dec 02 2020

Mathematica

a[1] = 1; a[n_] := -Sum[Sum[j DivisorSigma[0, j], {j, Divisors[n/d]}] a[d], {d, Most @ Divisors[n]}]; Table[a[n], {n, 1, 60}]
f[p_, e_] := Which[e==1, -(2*p+1), e==2, p^2+2*p, e==3, -p^2, e>3, 0]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Dec 02 2020 *)

Crossrefs

Cf. A046101 (positions of 0's), A046692, A055615, A060640, A101035.

Sequence in context: A154370 A045251 A099497 * A347127 A061813 A173664

Adjacent sequences: A327957 A327958 A327959 * A327961 A327962 A327963

Keyword

sign,mult

Author

Ilya Gutkovskiy, Oct 22 2019

Status

approved