A342432 - OEIS

%I #22 May 23 2021 07:28:00

%S 1,2,5,22,129,1411,16813,266372,4787349,100391653,2357947701,

%T 61980047702,1792160394049,56707753687079,1946197516142925,

%U 72061992621375496,2862423051509815809,121441389759089405193,5480386857784802185957

%N a(n) = Sum_{k=1..n} gcd(k,n)^(n-2).

%H Seiichi Manyama, <a href="/A342432/b342432.txt">Table of n, a(n) for n = 1..388</a>

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

%F a(n) = Sum_{d|n} mu(n/d) * d * sigma_(n-3)(d).

%F a(n) ~ n^(n-2). - _Vaclav Kotesovec_, May 23 2021

%t a[n_] := Sum[GCD[k, n]^(n - 2), {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Mar 12 2021 *)

%o (PARI) a(n) = sum(k=1, n, gcd(k, n)^(n-2));

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

%o (PARI) a(n) = sumdiv(n, d, moebius(n/d)*d*sigma(d, n-3));

%Y Cf. A000010, A332517, A342412, A342433, A343510.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 12 2021