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%I #17 Mar 20 2021 11:35:16
%S 1,2,4,5,8,10,12,14,28,28,20,62,24,54,272,68,32,198,36,676,1224,130,
%T 44,1348,4136,180,3540,3426,56,12632,60,1640,22520,304,129456,22370,
%U 72,378,101808,270952,80,192996,84,40630,1867184,550,92,551528,1679700,4198860,2105408
%N a(n) = Sum_{k=1..n} phi(gcd(k, n))^(n/gcd(k, n)).
%H Seiichi Manyama, <a href="/A342541/b342541.txt">Table of n, a(n) for n = 1..5000</a>
%F a(n) = Sum_{d|n} phi(n/d) * phi(d)^(n/d).
%F If p is prime, a(p) = 2 *(p-1).
%t a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(n/#) &]; Array[a, 50] (* _Amiram Eldar_, Mar 15 2021 *)
%o (PARI) a(n) = sum(k=1, n, eulerphi(gcd(k, n))^(n/gcd(k, n)));
%o (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*eulerphi(d)^(n/d));
%Y Cf. A000010, A029935, A342485, A342539, A342542, A342543.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Mar 15 2021
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