This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056583 #10 Jan 22 2025 14:28:37
%S A056583 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 A056583 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 A056583 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 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.
%H A056583 Antti Karttunen, <a href="/A056583/b056583.txt">Table of n, a(n) for n = 2..20000</a>
%F A056583 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 A056583 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.
%o A056583 (PARI) A056583(n) = if(2==n, 1, if(4==n, 0, if(8==n, 16, if(9==n, 27, if(isprime(n), 1, if(!(n%2) && isprime(n/2), 2*n, n)))))); \\ _Antti Karttunen_, Jan 22 2025
%Y A056583 Cf. A000312, A002109, A056582, A056584.
%K A056583 nonn
%O A056583 2,5
%A A056583 _Henry Bottomley_, Jul 03 2000