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%I #3 Jun 13 2021 14:17:50
%S 0,1,1,4,1,5,1,16,27,7,1,40,1,9,8,64,1,225,1,104,10,13,1,152,3125,15,
%T 729,200,1,31,1,256,14,19,12,2052,1,21,16,408,1,41,1,488,3384,25,1,
%U 592,823543,100025,20,680,1,5859,16,792,22,31,1,932,1,33,9270,1024,18,61,1
%N a(n) = Sum_{p|n} (n/p)^gcd(p,n/p).
%C a(p) = Sum_{p|p} (p/p)^gcd(p,p/p) = 1^1 = 1 for primes p.
%e a(10) = Sum_{p|10} (10/p)^gcd(p,10/p) = 5^gcd(2,5) + 2^gcd(5,2) = 5^1 + 2^1 = 7.
%t Table[Sum[(n/k)^GCD[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
%K nonn
%O 1,4
%A _Wesley Ivan Hurt_, Jun 13 2021
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