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%I #13 Aug 05 2018 20:44:35
%S 1,24,-252,2048,-4830,-6048,16744,0,177147,-115920,-534612,-516096,
%T 577738,401856,1217160,0,6905934,4251528,-10661420,-9891840,-4219488,
%U -12830688,-18643272,0,48828125,13865712,0,34291712,-128406630,29211840
%N Dirichlet inverse of Ramanujan's L-series (A000594).
%C Although it is conjectured that A000594(n) is never 0 here a(n)=0 for infinitely many n. Namely a(n)=0 iff n is not cubefree (n is in A046099).
%C Multiplicative because A000594 is. - _Andrew Howroyd_, Aug 05 2018
%D B. Cloitre, On the order of absolute convergence of Dirichlet series and the Grand Riemann hypothesis, in preparation 2010-2011 (unpublished as of August 2018).
%H Andrew Howroyd, <a href="/A181104/b181104.txt">Table of n, a(n) for n = 1..1000</a>
%F For Re(s)>13/2 we have sum_{n>0}a(n)/n^s*sum_{n>0}A000594(n)/n^s=1. If n is squarefree then a(n)=(-1)^omega(n)*A000594(n).
%t a[1] = 1; a[n_] := a[n] = -Sum[a[d]*RamanujanTau[n/d], {d, Most[Divisors[n]]}]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Jun 18 2013 *)
%o (PARI) a(n)=if(n<2,1/A000594(1),-1/A000594(1)*sumdiv(n,d,if(n-d,a(d)*A000594(n/d),0)))
%o (PARI) seq(n)={dirdiv(vector(n, n, n==1), vector(n, n, ramanujantau(n)))} \\ _Andrew Howroyd_, Aug 05 2018
%Y Cf. A000594, A046099
%K sign,mult
%O 1,2
%A _Benoit Cloitre_, Oct 03 2010
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