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 A373240 #23 Jun 21 2024 15:20:05 %S A373240 60,12,2,24,6,8,12,3,4,12,6,8,6,24,4,3,12,4,6,24,2,24,12,1 %N A373240 Greatest common divisor of the product of terms in positive Pythagorean n-tuples, over all possible such tuples. %C A373240 A Pythagorean n-tuple consists of positive integers X1,...,Xn where X1^2 + X2^2 + ... + X(n-1)^2 = Xn^2. The product of those terms is P = X1*X2*...*Xn. %C A373240 a(n) is the GCD of all possible products P arising this way. %C A373240 If n is odd, then 2 | a(n). %C A373240 If n mod 3 is 0 or 1, then 3 | a(n). %C A373240 If n is divisible by 4, then 4 | a(n). %C A373240 If n mod 8 is 1 or 3, then 4 | a(n). %C A373240 If n mod 8 is 0 or 6, then 8 | a(n). %C A373240 If n mod 24 is 2, then a(n)=1. %C A373240 a(n+24)=a(n) for n >= 4. %H A373240 Des MacHale and Christian van den Bosch, <a href="https://www.jstor.org/stable/23249521">Generalising a result about Pythagorean triples</a>, The Mathematical Gazette, Vol. 96, March 2012. %e A373240 For n = 8, then 8 | a(n). Since 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 2^2 + 2^2 = 4^2 with P = 1*1*1*1*2*2*2*4 = 32 and 1^2 + 1^2 + 1^2 + 1^2 + 1^2 + 2^2 + 4^2 = 5^2 with P = 1*1*1*1*1*2*4*5 = 40, then a(8) = gcd(32,40) = 8, and no larger number will divide the product of terms in every Pythagorean octuple. %K A373240 nonn,more %O A373240 3,1 %A A373240 _Brian Almond_, May 28 2024