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

1, 1, 2, 12, 12, 360, 60, 1680, 2520, 25200, 2520, 332640, 27720, 5045040, 5405400, 2882880, 720720, 220540320, 12252240, 4655851200, 4888643760, 5121436320, 232792560, 128501493120, 26771144400, 696049754400

Offset: 1

Author

Andrew Weimholt, Jul 05 2010

Keywords

• nonn
• nice

Comments

From Robert Israel, Dec 29 2017: (Start)

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.

Otherwise, a(n) = n^2*Product_p p^floor(log_p(n/p^(nu(n,p)))),

where the product is over all primes p < n and nu(n,p) is the p-adic order of n. (End)

Examples

			After a(1)=a(2)=1, we must have a(3) >= 2 from 2 | a(1+2), and a(3)=2 works.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2293

Programs

Maple

seq(ilcm(seq(x*(n-x),x=1..n/2)),n=1..50); # Robert Israel, Dec 28 2017

Mathematica

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 *)