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%I #14 Mar 05 2022 01:37:36
%S 1,-2,-3,-1,-7,1,-13,-5,-10,5,-29,7,-37,11,-1,2,-53,29,-61,11,7,43,
%T -79,37,-40,51,-14,35,-107,103,-113,5,43,75,43,41,-151,87,59,97,-173,
%U 169,-181,43,142,119,-199,50,-54,157,89,81,-239,170,155,151,103,159,-271,41,-281,169,276,59,207
%N a(1) = 1; a(n) = -Sum_{d|n, d > 1} prime(d-1) * a(n/d).
%C Dirichlet inverse of A008578.
%H Ilya Gutkovskiy, <a href="/A352062/a352062.jpg">Scatterplot of a(n) up to n=50000</a>
%t a[1] = 1; a[n_] := a[n] = -Sum[If[d > 1, Prime[d - 1] a[n/d], 0], {d, Divisors[n]}]; Table[a[n], {n, 65}]
%Y Cf. A008578, A030013, A030014, A034759.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, Mar 04 2022