A334744 a(1) = 1; a(n) = -Sum_{d|n, d < n} bigomega(n/d) * a(d), where bigomega = A001222.
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
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..20000
- Eric Weisstein's World of Mathematics, Prime Factor
Programs
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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}] -
PARI
memoA334744 = Map(); A334744(n) = if(1==n,1,my(v); if(mapisdefined(memoA334744,n,&v), v, v = -sumdiv(n,d,if(d
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)).
Comments