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 A129365 #10 Feb 06 2024 11:30:23
%S A129365 1,1,1,1,1,2,2,2,6,48,48,48,48,1536,207360,207360,207360,1105920,
%T A129365 1105920,17694720,30098718720,15410543984640,15410543984640,
%U A129365 481579499520,60197437440000,123284351877120000,29958097506140160000
%N A129365 a(n) = A092287(n)/A129364(n).
%C A129365 Conjectures:
%C A129365 A) a(n) is always an integer.
%C A129365 B) If p is a prime then p|a(n) if and only if p <= n/3. Let ordp(n,p) denote the exponent of the largest power of p which divides n. For example, ordp(48,2) = 4 since 48 = 3*(2^4). The precise decomposition of a(n) into primes would follow from the following two conjectures:
%C A129365 C) For each positive integer n and prime p, ordp(a(n*p),p) = ordp(a(n*p+1),p) = ordp(a(n*p+2),p) = . . . = ordp(a(n*p+p-1),p).
%C A129365 D) Let b(n) = A004125(n). Then ordp(a(n*p),p) = b(n) + b(floor(n/p)) + b(floor(n/p^2)) + b(floor(n/p^3)) + .... This is reminiscent of de Polignac's formula (also due to Legendre) for the prime factorization of n! (see the link).
%H A129365 Wikipedia, <a href="http://en.wikipedia.org/wiki/De_Polignac%27s_formula">De Polignac's formula</a>.
%F A129365 a(n) = ( Product_{j = 1..n} Product_{k = 1..n} gcd(j,k) ) / ( Product_{j = 1..n} Product_{d|j} d^(j/d) ).
%F A129365 a(n) = ( Product_{j = 1..n} Product_{k = 1..n} gcd(j,k) ) / ( Product_{k = 1..n} (floor(n/k)!)^k ).
%Y A129365 Cf. A004125, A092287, A129364.
%K A129365 easy,nonn
%O A129365 1,6
%A A129365 _Peter Bala_, Apr 13 2007