A342489 a(n) = Sum_{d|n} phi(d)^(d-1).

1, 2, 5, 10, 257, 38, 46657, 16394, 1679621, 262402, 10000000001, 4194350, 8916100448257, 13060740674, 4398046511365, 35184372105226, 18446744073709551617, 16926661124390, 39346408075296537575425, 144115188076118282, 3833759992447475168837

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, A014566, A164941, A342473, A342485.

Programs

Mathematica

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

PARI

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

PARI

a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^(n/gcd(k, n)-2));

PARI

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

Formula

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

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

If p is prime, a(p) = 1 + (p-1)^(p-1) = A014566(p-1).