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 A342620 a(n) = Sum_{d|n} phi(n/d)^(n+d+1). 2

%I

%S 1,2,33,66,16385,770,10077697,1050626,362805249,83886082,

%T 10000000000001,268664834,15407021574586369,19747769352194,

%U 2252074693689345,18014673389486082,75557863725914323419137,25593109118189570,229468251895129407139872769,73788172563556335618,6624765697237267477692417,11000000000000000000000002

%N a(n) = Sum_{d|n} phi(n/d)^(n+d+1).

%H Seiichi Manyama, <a href="/A342620/b342620.txt">Table of n, a(n) for n = 1..388</a>

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

%F G.f.: Sum_{k>=1} phi(k)^(k+2) * x^k/(1 - phi(k)^(k+1) * x^k).

%F If p is prime, a(p) = 1 + (p-1)^(p+2).

%t a[n_] := DivisorSum[n, EulerPhi[n/#]^(n + # + 1) &]; Array[a, 20] (* _Amiram Eldar_, Mar 17 2021 *)

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

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

%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^(k+2)*x^k/(1-eulerphi(k)^(k+1)*x^k)))

%Y Cf. A000010, A342613.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 16 2021

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Last modified December 3 22:32 EST 2021. Contains 349468 sequences. (Running on oeis4.)