OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..16384
FORMULA
G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} psi(k) * A(x^k). - Ilya Gutkovskiy, Sep 04 2019
From Amiram Eldar, Oct 14 2020: (Start)
Multiplicative with a(p^e) = (-1)^e * (p+1).
Dirichlet g.f.: zeta(2*s)/(zeta(s-1)*zeta(s)). - Amiram Eldar, Dec 05 2022
MATHEMATICA
psi[n_] := If[n == 1, 1, n Times @@ (1 + 1/FactorInteger[n][[All, 1]])];
a[n_] := a[n] = If[n == 1, 1, -Sum[psi[n/d] a[d], {d, Most@ Divisors[n]}]];
Array[a, 75] (* Jean-François Alcover, Feb 15 2020 *)
f[p_, e_] := (-1)^e * (p + 1); a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Oct 14 2020 *)
PROG
CROSSREFS
KEYWORD
sign,mult,easy
AUTHOR
Antti Karttunen, Jan 13 2019
STATUS
approved