A334744 - OEIS

%I #4 May 09 2020 19:18:09

%S 1,-1,-1,-1,-1,0,-1,0,-1,0,-1,2,-1,0,0,1,-1,2,-1,2,0,0,-1,2,-1,0,0,2,

%T -1,3,-1,1,0,0,0,2,-1,0,0,2,-1,3,-1,2,2,0,-1,-1,-1,2,0,2,-1,2,0,2,0,0,

%U -1,0,-1,0,2,0,0,3,-1,2,0,3,-1,-3,-1,0,2,2,0,3,-1,-1,1,0,-1,0,0,0,0,2,-1,0,0,2

%N a(1) = 1; a(n) = -Sum_{d|n, d < n} bigomega(n/d) * a(d), where bigomega = A001222.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeFactor.html">Prime Factor</a>

%F G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} bigomega(k) * A(x^k).

%F Dirichlet g.f.: 1 / (1 + zeta(s) * Sum_{k>=1} primezeta(k*s)).

%t a[n_] := If[n == 1, n, -Sum[If[d < n, PrimeOmega[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 92}]

%Y Cf. A001222, A007427, A069513, A327276, A334743.

%K sign

%O 1,12

%A _Ilya Gutkovskiy_, May 09 2020