A342424 a(n) = Sum_{k=1..n} gcd(k,n)^(n/gcd(k,n)).

1, 3, 5, 10, 9, 33, 13, 60, 69, 167, 21, 470, 25, 837, 1245, 1624, 33, 5067, 37, 9570, 13841, 20633, 45, 54612, 12545, 98511, 119601, 201646, 57, 562957, 61, 794928, 1774185, 2097491, 536037, 5381754, 73, 9437601, 19136333, 14296940

Offset: 1

Author

Seiichi Manyama, Mar 11 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000010, A332517, A342423.

Programs

Mathematica

a[n_] := Sum[GCD[k, n]^(n/GCD[k, n]), {k, 1, n}]; Array[a, 40] (* Amiram Eldar, Mar 11 2021 *)

PARI

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

PARI

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

Formula

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