A164941 a(n) = Sum_{d|n} phi(n/d)^(d-1).

1, 2, 2, 3, 2, 5, 2, 5, 6, 7, 2, 17, 2, 9, 34, 15, 2, 45, 2, 87, 102, 13, 2, 191, 258, 15, 294, 289, 2, 1579, 2, 203, 1126, 19, 5394, 2577, 2, 21, 4242, 17227, 2, 16083, 2, 2037, 83282, 25, 2, 36107, 46658, 262423, 65794, 5839, 2, 139161, 1058578, 292455

Offset: 1

Author

Franklin T. Adams-Watters, Sep 01 2009

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000010, A087909, A309369.

Programs

PARI

a(n) = sumdiv(n, d, eulerphi(d)^(n/d-1)); \\ Seiichi Manyama, Mar 13 2021

PARI

a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(gcd(k, n)-2)); \\ Seiichi Manyama, Mar 13 2021

PARI

my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-eulerphi(k)*x^k))) \\ Seiichi Manyama, Mar 13 2021

Formula

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

From Seiichi Manyama, Mar 13 2021: (Start)

a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^(gcd(k, n) - 2).

If p is prime, a(p) = 2. (End)