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a(n) = Sum_{k=1..n} phi(gcd(k, n))^(n/gcd(k, n) - 1).
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%I #19 Mar 19 2021 07:02:07

%S 1,2,3,4,5,7,7,9,15,13,11,33,13,19,105,33,17,91,19,209,469,31,23,641,

%T 1045,37,1627,841,29,4217,31,673,10461,49,29785,10281,37,55,49465,

%U 68769,41,65197,43,12281,529625,67,47,273185,279979,1049661,1049121,52657,53,803647

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

%H Seiichi Manyama, <a href="/A342542/b342542.txt">Table of n, a(n) for n = 1..5000</a>

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

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

%t a[n_] := DivisorSum[n, EulerPhi[n/#] * EulerPhi[#]^(n/#-1) &]; Array[a, 50] (* _Amiram Eldar_, Mar 15 2021 *)

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

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

%Y Cf. A000010, A029935, A342473, A342540, A342541, A342544.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Mar 15 2021