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A342617 a(n) = Sum_{d|n} phi(d)^(n-d+1). 1

%I #16 Mar 18 2021 08:25:00

%S 1,2,3,4,5,20,7,38,135,4102,11,1670,13,1679624,4202505,270346,17,

%T 60539912,19,4299292682,470185508877,1000000000012,23,17253793802,

%U 4398046511125,1283918464548878,609359773564947,131622174060806158,29,4789472952582154,31

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

%H Seiichi Manyama, <a href="/A342617/b342617.txt">Table of n, a(n) for n = 1..605</a>

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

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

%F If p is prime, a(p) = p.

%t a[n_] := DivisorSum[n, EulerPhi[#]^(n - # + 1) &]; Array[a, 30] (* _Amiram Eldar_, Mar 17 2021 *)

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

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

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

%Y Cf. A000010, A342607.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 16 2021

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Last modified July 19 20:58 EDT 2024. Contains 374436 sequences. (Running on oeis4.)