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a(n) = Sum_{k=1..n} phi(gcd(k, n))^(gcd(k, n) - 1).
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%I #17 Mar 19 2021 07:00:48

%S 1,2,6,11,260,40,46662,16398,1679630,262408,10000000010,4194366,

%T 8916100448268,13060740684,4398046511640,35184372105244,

%U 18446744073709551632,16926661124436,39346408075296537575442,144115188076118572,3833759992447475215524,1000000000010000000020

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

%H Seiichi Manyama, <a href="/A342544/b342544.txt">Table of n, a(n) for n = 1..388</a>

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

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

%t a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(# - 1) &]; Array[a, 20] (* _Amiram Eldar_, Mar 15 2021 *)

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

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

%Y Cf. A000010, A029935, A309369, A342436, A342540, A342542, A342543.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 15 2021