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A169900 Earliest sequence such that xy | a(x+y) for all x>=1, y>=1.

%I A169900 #13 Dec 29 2017 02:52:58
%S A169900 1,1,2,12,12,360,60,1680,2520,25200,2520,332640,27720,5045040,5405400,
%T A169900 2882880,720720,220540320,12252240,4655851200,4888643760,5121436320,
%U A169900 232792560,128501493120,26771144400,696049754400
%N A169900 Earliest sequence such that xy | a(x+y) for all x>=1, y>=1.
%C A169900 From _Robert Israel_, Dec 29 2017: (Start)
%C A169900 If n = p^d for prime p, then a(n) = p^(2*d-2)*Product_q q^floor(log_q(n)), where the product is over all primes q < n other than p.
%C A169900 Otherwise, a(n) = n^2*Product_p p^floor(log_p(n/p^(nu(n,p)))),
%C A169900  where the product is over all primes p < n and nu(n,p) is the p-adic order of n. (End)
%H A169900 Robert Israel, <a href="/A169900/b169900.txt">Table of n, a(n) for n = 1..2293</a>
%e A169900 After a(1)=a(2)=1, we must have a(3) >= 2 from 2 | a(1+2), and a(3)=2 works.
%p A169900 seq(ilcm(seq(x*(n-x),x=1..n/2)),n=1..50); # _Robert Israel_, Dec 28 2017
%t A169900 a[n_]:=If[n<=2,1,LCM@@Table[x(n-x),{x,Floor[n/2]}]];Table[a[n],{n,30}] (* _Zak Seidov_, Jul 11 2010 *)
%K A169900 nonn,nice
%O A169900 1,3
%A A169900 _Andrew Weimholt_, Jul 05 2010