A383000 a(n) = Sum_{d|n} phi(n/d) * (-3)^(d-1).

1, -2, 11, -28, 85, -238, 735, -2216, 6585, -19610, 59059, -177428, 531453, -1593606, 4783175, -14351152, 43046737, -129134082, 387420507, -1162281100, 3486785925, -10460294174, 31381059631, -94143360856, 282429536825, -847288078026, 2541865841523, -7625599078020, 22876792454989

Offset: 1

Author

Seiichi Manyama, Apr 12 2025

Keywords

• sign

Crossrefs

Column k=3 of A382995.

Cf. A000010, A034754, A343465.

Programs

PARI

a(n) = sumdiv(n, d, eulerphi(n/d)*(-3)^(d-1));

Formula

a(n) = Sum_{k=1..n} (-3)^(gcd(n,k) - 1).

G.f.: Sum_{k>=1} phi(k) * x^k / (1 + 3*x^k).