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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
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
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 09 2020
STATUS
approved