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%I #27 May 11 2021 10:58:44
%S 1,5,10,99,36,4290,134,72613,20713,1053700,2058,2194638822,8204,
%T 268550150,1073938440,156969213515,131088,101697785139535,524306,
%U 3657271905119820,4398063288332,17592232181770,8388630,4727105990672866963914,847422827191,4503600499785740
%N a(n) = Sum_{x_1|n, x_2|n, ... , x_n|n} gcd(x_1,x_2, ... ,x_n).
%H Seiichi Manyama, <a href="/A344140/b344140.txt">Table of n, a(n) for n = 1..719</a>
%F a(n) = Sum_{x_1|n, x_2|n, ... , x_n|n} n/lcm(x_1,x_2, ... ,x_n).
%F a(n) = Sum_{d|n} phi(n/d) * tau(d)^n.
%F If p is prime, a(p) = 2^p - 1 + p.
%F a(n) = Sum_{k=1..n} tau(gcd(k,n))^n.
%t a[n_] := DivisorSum[n, EulerPhi[n/#] * DivisorSigma[0, #]^n &]; Array[a, 20] (* _Amiram Eldar_, May 10 2021 *)
%o (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d)^n);
%o (PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n))^n);
%Y Cf. A000203, A060724, A344080, A344132, A344138, A344139.
%K nonn
%O 1,2
%A _Seiichi Manyama_, May 10 2021
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