A342487 a(n) = Sum_{d|n} phi(d)^(n+1).

1, 2, 17, 34, 4097, 258, 1679617, 262658, 60467201, 8388610, 1000000000001, 67133442, 1283918464548865, 940369969154, 281479271743489, 2251816993685506, 4722366482869645213697, 1218719481069570, 12748236216396078174437377, 9223380832949895170

Offset: 1

Author

Seiichi Manyama, Mar 13 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..388

Crossrefs

Cf. A000010, A342471, A342485, A342488, A342490.

Programs

Mathematica

a[n_] := DivisorSum[n, EulerPhi[#]^(n+1) &]; Array[a, 20] (* Amiram Eldar, Mar 14 2021 *)

PARI

a(n) = sumdiv(n, d, eulerphi(d)^(n+1));

PARI

a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^n);

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^(k+1)*x^k/(1-(eulerphi(k)*x)^k)))

Formula

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

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

If p is prime, a(p) = 1 + (p-1)^(p+1).