A334743 a(1) = 1; a(n) = -Sum_{d|n, d < n} omega(n/d) * a(d), where omega = A001221.

1, -1, -1, 0, -1, 0, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 3, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 3, -1, 1, 1, 0, -1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, -1, -1, -1, 0, 1, 0, 0, 3, -1, 1, 0, 3, -1, -1, -1, 0, 1, 1, 0, 3, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1

Offset

1,30

Comments

Dirichlet inverse of A087802. - Antti Karttunen, Nov 29 2024

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Eric Weisstein's World of Mathematics, Distinct Prime Factors

Formula

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

Dirichlet g.f.: 1 / (1 + zeta(s) * primezeta(s)).

Mathematica

a[n_] := If[n == 1, n, -Sum[If[d < n, PrimeNu[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 90}]

Prog

(PARI)
memoA334743 = Map();
A334743(n) = if(1==n, 1, my(v); if(mapisdefined(memoA334743, n, &v), v, v = -sumdiv(n, d, if(d<n, omega(n/d)*A334743(d), 0)); mapput(memoA334743, n, v); (v))); \\ Antti Karttunen, Nov 29 2024

Crossrefs

Cf. A001221, A007427, A008480, A008683, A010051, A087802 (Dirichlet inverse), A327276, A334744.

Sequence in context: A060282 A060283 A255851 * A078529 A180017 A243827

Adjacent sequences: A334740 A334741 A334742 * A334744 A334745 A334746

Keyword

sign

Author

Ilya Gutkovskiy, May 09 2020

Status

approved