A162868 Least common multiple of all squares and all sums of two squares up to n^2 + n^2.

1, 2, 40, 4680, 1591200, 1891936800, 4270101357600, 11089453225687200, 32565776278494961756800, 28429922691126101613686400, 42204464874461454985621846571472000

Offset: 0

Author

Carl R. White, Jul 15 2009

Keywords

• easy
• nonn

Comments

Also the least common multiple of all rows of triangle A069011 up to the n-th row.

lcm(0) is taken to be 1, which follows from 0! = 1.

Examples

			a(3) = lcm(0^2+0^2; 0^2+1^2, 1^2+1^2; 0^2+2^2, 1^2+2^2, 2^2+2^2; 0^2+3^2, 1^2+3^2, 2^2+3^2, 3^2+3^2) = lcm(0; 1, 2; 4, 5, 8; 9, 10, 13, 18) = 4680.
		

Crossrefs

Cf. A069011, A001481.

Programs

PARI

a(n) = {mcl = 1; for (x = 0, n, for (y = 0, n, if (v = x^2+y^2, mcl = lcm(mcl, v)););); mcl;} \\ Michel Marcus, Sep 03 2013

Formula

a(n) = lcm({ x,y:N | 0 <= x <= y <= n; x^2+y^2 })