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A342488 a(n) = Sum_{d|n} phi(d)^(n/d+1).

%I A342488 #25 May 09 2021 08:06:25
%S A342488 1,2,5,6,17,14,37,26,53,82,101,74,145,254,385,162,257,398,325,1218,
%T A342488 1697,1102,485,1058,4497,1874,2645,8394,785,19330,901,2306,14497,4354,
%U A342488 112769,17738,1297,6158,37697,270082,1601,316130,1765,105498,1165441,11134,2117,162050,1681381
%N A342488 a(n) = Sum_{d|n} phi(d)^(n/d+1).
%H A342488 Seiichi Manyama, <a href="/A342488/b342488.txt">Table of n, a(n) for n = 1..8299</a>
%F A342488 a(n) = Sum_{k=1..n} phi(n/gcd(k, n))^gcd(k, n).
%F A342488 G.f.: Sum_{k>=1} phi(k)^2 * x^k/(1 - phi(k) * x^k).
%F A342488 If p is prime, a(p) = 1 + (p-1)^2 = A002522(p-1).
%F A342488 a(n) = Sum_{k=1..n} phi(gcd(k, n))^(n/gcd(k, n) + 1)/phi(n/gcd(k, n)). - _Richard L. Ollerton_, May 07 2021
%t A342488 a[n_] := DivisorSum[n, EulerPhi[#]^(n/#+1) &]; Array[a, 50] (* _Amiram Eldar_, Mar 14 2021 *)
%o A342488 (PARI) a(n) = sumdiv(n, d, eulerphi(d)^(n/d+1));
%o A342488 (PARI) a(n) = sum(k=1, n, eulerphi(n/gcd(k, n))^gcd(k, n));
%o A342488 (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, eulerphi(k)^2*x^k/(1-eulerphi(k)*x^k)))
%Y A342488 Cf. A000010, A002522, A164941, A309369, A342485, A342487.
%K A342488 nonn
%O A342488 1,2
%A A342488 _Seiichi Manyama_, Mar 13 2021