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%I #45 Dec 02 2020 03:15:40
%S 1,-5,-7,8,-11,35,-15,-4,15,55,-23,-56,-27,75,77,0,-35,-75,-39,-88,
%T 105,115,-47,28,35,135,-9,-120,-59,-385,-63,0,161,175,165,120,-75,195,
%U 189,44,-83,-525,-87,-184,-165,235,-95,0,63,-175,245,-216,-107,45,253,60,273,295,-119,616
%N Dirichlet g.f.: 1 / (zeta(s) * zeta(s-1)^2).
%C Dirichlet inverse of A060640.
%C Moebius transform applied twice to A101035.
%H Amiram Eldar, <a href="/A327960/b327960.txt">Table of n, a(n) for n = 1..10000</a>
%F a(1) = 1; a(n) = -Sum_{d|n, d<n} A060640(n/d) * a(d).
%F a(n) = Sum_{d|n} A046692(n/d) * A055615(d).
%F 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
%t 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}]
%t 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 *)
%Y Cf. A046101 (positions of 0's), A046692, A055615, A060640, A101035.
%K sign,mult
%O 1,2
%A _Ilya Gutkovskiy_, Oct 22 2019
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