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A328722 Dirichlet g.f.: 1 / zeta(s-1)^2. 0

%I

%S 1,-4,-6,4,-10,24,-14,0,9,40,-22,-24,-26,56,60,0,-34,-36,-38,-40,84,

%T 88,-46,0,25,104,0,-56,-58,-240,-62,0,132,136,140,36,-74,152,156,0,

%U -82,-336,-86,-88,-90,184,-94,0,49,-100,204,-104,-106,0,220,0,228,232,-118,240

%N Dirichlet g.f.: 1 / zeta(s-1)^2.

%C Dirichlet inverse of A038040.

%C Dirichlet convolution of A055615 with itself.

%C Moebius transform of A101035.

%F a(1) = 1; a(n) = -Sum_{d|n, d<n} A038040(n/d) * a(d).

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

%F a(n) = Sum_{d|n} mu(n/d) * A101035(d).

%t a[1] = 1; a[n_] := -Sum[(n/d) DivisorSigma[0, n/d] a[d], {d, Most @ Divisors[n]}]; Table[a[n], {n, 1, 60}]

%t Table[n DivisorSum[n, MoebiusMu[n/#] MoebiusMu[#] &], {n, 1, 60}]

%Y Cf. A007427, A008683, A038040, A046099 (positions of 0's), A055615, A101035.

%K sign,mult

%O 1,2

%A _Ilya Gutkovskiy_, Oct 26 2019

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Last modified August 6 11:36 EDT 2020. Contains 336246 sequences. (Running on oeis4.)