A342433 - OEIS

%I #24 May 23 2021 07:27:23

%S 1,3,11,74,629,8085,117655,2113796,43059849,1001955177,25937424611,

%T 743379914746,23298085122493,793811662313709,29192938251553759,

%U 1152956691126550536,48661191875666868497,2185928270773974154773

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

%H Seiichi Manyama, <a href="/A342433/b342433.txt">Table of n, a(n) for n = 1..387</a>

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

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

%F a(n) ~ n^(n-1). - _Vaclav Kotesovec_, May 23 2021

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

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

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

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

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

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 12 2021