A342433 a(n) = Sum_{k=1..n} gcd(k,n)^(n-1).

1, 3, 11, 74, 629, 8085, 117655, 2113796, 43059849, 1001955177, 25937424611, 743379914746, 23298085122493, 793811662313709, 29192938251553759, 1152956691126550536, 48661191875666868497, 2185928270773974154773

Offset: 1

Author

Seiichi Manyama, Mar 12 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..387

Crossrefs

Cf. A000010, A000272, A321349, A332517, A332621, A342432, A343510.

Programs

Mathematica

a[n_] := Sum[GCD[k, n]^(n - 1), {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 12 2021 *)

PARI

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

PARI

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

PARI

a(n) = sumdiv(n, d, moebius(n/d)*d*sigma(d, n-2));

Formula

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

a(n) = Sum_{d|n} mu(n/d) * d * sigma_(n-2)(d).

a(n) ~ n^(n-1). - Vaclav Kotesovec, May 23 2021