A342543 - OEIS

%I #17 Mar 15 2021 10:59:18

%S 1,2,10,19,1028,76,279942,65558,10077718,1049608,100000000010,

%T 16777334,106993205379084,78364444044,35184372090920,281474976776236,

%U 295147905179352825872,101559966746268,708235345355337676357650,1152921504607897676,46005119909369702026044,10000000000100000000020

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

%H Seiichi Manyama, <a href="/A342543/b342543.txt">Table of n, a(n) for n = 1..388</a>

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

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

%t a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^# &]; Array[a, 20] (* _Amiram Eldar_, Mar 15 2021 *)

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

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

%Y Cf. A000010, A029935, A342423, A342488, A342539, A342541, A342544.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 15 2021