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%I #19 May 11 2021 10:35:08
%S 1,5,10,87,36,4114,134,65629,19705,1048628,2058,2176786622,8204,
%T 268435614,1073741928,152587956347,131088,101559956696337,524306,
%U 3656158441111964,4398046511420,17592186046514,8388630,4722366482871822135514,847288609591,4503599627378748
%N a(n) = Sum_{k=1..n} tau(gcd(k,n))^gcd(k,n), where tau(n) is the number of divisors of n.
%F a(n) = Sum_{d|n} phi(n/d) * tau(d)^d.
%F If p is prime, a(p) = 2^p - 1 + p.
%t a[n_] := DivisorSum[n, EulerPhi[n/#] * DivisorSigma[0, #]^# &]; Array[a, 26] (* _Amiram Eldar_, May 11 2021 *)
%o (PARI) a(n) = sum(k=1, n, numdiv(gcd(k, n))^gcd(k, n));
%o (PARI) a(n) = sumdiv(n, d, eulerphi(n/d)*numdiv(d)^d);
%Y Cf. A000005, A342423, A344081, A344140, A344195.
%K nonn
%O 1,2
%A _Seiichi Manyama_, May 11 2021
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