OFFSET
1,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
a(n) is multiplicative with a(2) = 1, a(2^e) = 6*4^(e-2) if e>1. a(p) = -p, a(p^e) = 0 if e>1, p>2.
G.f. A(x) satisfies -x * (1 - x) = Sum_{k>=1} (-1)^k * k * A(x^k).
MATHEMATICA
f[p_, e_] := If[e == 1, -p, 0]; f[2, e_] := If[e == 1, 1, 6*4^(e-2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, May 09 2023 *)
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Seiichi Manyama, Apr 02 2023
STATUS
approved