A342449 a(n) = Sum_{k=1..n} gcd(k,n)^k.

1, 5, 29, 262, 3129, 46705, 823549, 16777544, 387421251, 10000003469, 285311670621, 8916100581446, 302875106592265, 11112006826387025, 437893890391180013, 18446744073743123788, 827240261886336764193, 39346408075299116257065

Offset: 1

Author

Seiichi Manyama, Mar 13 2021

Keywords

• nonn

Crossrefs

Cf. A000010, A001923, A018804, A050873, A231712, A332517, A341036, A342370, A342389, A342423.

Programs

Mathematica

a[n_] := Sum[GCD[k, n]^k, {k, 1, n}]; Array[a, 20] (* Amiram Eldar, Mar 13 2021 *)

PARI

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

Formula

If p is prime, a(p) = p-1 + p^p = A231712(p).