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 A334744 a(1) = 1; a(n) = -Sum_{d|n, d < n} bigomega(n/d) * a(d), where bigomega = A001222. 1
 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, -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, -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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 LINKS Eric Weisstein's World of Mathematics, Prime Factor FORMULA G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} bigomega(k) * A(x^k). Dirichlet g.f.: 1 / (1 + zeta(s) * Sum_{k>=1} primezeta(k*s)). MATHEMATICA a[n_] := If[n == 1, n, -Sum[If[d < n, PrimeOmega[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 92}] CROSSREFS Cf. A001222, A007427, A069513, A327276, A334743. Sequence in context: A343220 A264893 A340653 * A136567 A336569 A324904 Adjacent sequences:  A334741 A334742 A334743 * A334745 A334746 A334747 KEYWORD sign AUTHOR Ilya Gutkovskiy, May 09 2020 STATUS approved

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Last modified May 14 16:48 EDT 2021. Contains 343898 sequences. (Running on oeis4.)