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A056583 Solution to a(n)^(n^2/a(n)) = gcd(n^n, Product_{k<n} k^k) where a(n) and n^2/a(n) are integers, or 0 if no such integers exist. 2

%I

%S 1,1,0,1,12,1,16,27,20,1,12,1,28,15,16,1,18,1,20,21,44,1,24,25,52,27,

%T 28,1,30,1,32,33,68,35,36,1,76,39,40,1,42,1,44,45,92,1,48,49,50,51,52,

%U 1,54,55,56,57,116,1,60,1,124,63,64,65,66,1,68,69,70,1,72,1,148,75,76

%N Solution to a(n)^(n^2/a(n)) = gcd(n^n, Product_{k<n} k^k) where a(n) and n^2/a(n) are integers, or 0 if no such integers exist.

%F a(2) = 1, a(4) = 0, a(8) = 16, a(9) = 27; if p an odd prime: a(p) = 1 and a(2p) = 4p; otherwise if n>1: a(n) = n. Apart from n = 4, a(n) = n^2/A056584(n) = A056582(n)^(1/A056584(n)).

%e For n = 4, there are no integer solutions of a^(16/a) = 4, though there are two real solutions of about 1.099997 and 43.55926.

%Y Cf. A000312, A002109, A056582, A056584.

%K nonn

%O 2,5

%A _Henry Bottomley_, Jul 03 2000

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