A342490 a(n) = Sum_{d|n} phi(d)^(n-1).

1, 2, 5, 10, 257, 66, 46657, 16514, 1679873, 524290, 10000000001, 4200450, 8916100448257, 26121388034, 4398314962945, 35185445863426, 18446744073709551617, 33853319151618, 39346408075296537575425, 144115737832194050, 3833763648605916233729, 2000000000000000000002

Offset

1,2

Links

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

Formula

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

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) = A014566(p-1).

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A014566, A342471, A342487.

Sequence in context: A133516 A342489 A342612 * A163784 A215615 A018862

Adjacent sequences: A342487 A342488 A342489 * A342491 A342492 A342493

Keyword

nonn

Author

Seiichi Manyama, Mar 13 2021

Status

approved