A342540 a(n) = Sum_{k=1..n} phi(gcd(k, n))^(n-1).

1, 2, 6, 11, 260, 68, 46662, 16518, 1680134, 524296, 10000000010, 4204550, 8916100448268, 26121388044, 4398583447560, 35185445896204, 18446744073709551632, 33853319413772, 39346408075296537575442, 144116012711673868, 3833767304764361539596, 2000000000000000000020

Offset

1,2

Links

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

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(n - 1) &]; Array[a, 20] (* Amiram Eldar, Mar 15 2021 *)

Prog

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

Crossrefs

Cf. A000010, A029935, A342471, A342539, A342542, A342544.

Sequence in context: A208893 A057294 A342544 * A328449 A293589 A293117

Adjacent sequences: A342537 A342538 A342539 * A342541 A342542 A342543

Keyword

nonn

Author

Seiichi Manyama, Mar 15 2021

Status

approved