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A128382 Inverse Moebius transform operation performed 24 times on A000594: A051731^24 * A000594.

%I A128382 #13 Sep 20 2019 08:55:42
%S A128382 1,0,276,-1748,4854,0,-16720,44552,-107295,0,534636,-482448,-577714,0,
%T A128382 1339704,2528206,-6905910,0,10661444,-8484792,-4614720,0,18643296,
%U A128382 12296352,-25383005,0,-75928312,29226560,128406654,0,-52843144,-151821160,147559536,0,-81158880
%N A128382 Inverse Moebius transform operation performed 24 times on A000594: A051731^24 * A000594.
%C A128382 Conjecture: given the inverse Moebius transform operation performed any k times (k=1,2,3,...); k=24 is the only such sequence with zeros. A weaker conjecture: "zero" occurs an infinite number of times in A128382.
%C A128382 Multiplicative because A000594 is. Each application of A051731 corresponds to an inverse Moebius transform. - _Andrew Howroyd_, Aug 03 2018
%H A128382 Andrew Howroyd, <a href="/A128382/b128382.txt">Table of n, a(n) for n = 1..1000</a>
%F A128382 Dirichlet g.f.: Sum_{n>=1} a(n)/n^s = (Sum_{n>=1} A000594(n)/n^s)*zeta(s)^24. - _Jianing Song_, Aug 04 2018
%t A128382 nmax = 40;
%t A128382 M = Table[If[Mod[n, k] == 0, 1, 0], {n, nmax}, {k, nmax}];
%t A128382 MatrixPower[M, 24].RamanujanTau[Range[nmax]] (* _Jean-François Alcover_, Sep 20 2019 *)
%o A128382 (PARI) seq(n, k=24)={my(u=vector(n,n,1), v=vector(n,n,ramanujantau(n))); for(i=1, k, v=dirmul(u,v)); v} \\ _Andrew Howroyd_, Aug 03 2018
%Y A128382 Cf. A051731, A000594, A128378, A128379, A128380, A128381.
%K A128382 sign,mult
%O A128382 1,3
%A A128382 _Gary W. Adamson_, Feb 28 2007
%E A128382 Terms a(11) and beyond from _Andrew Howroyd_, Aug 03 2018