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Least common multiple of all squares and all sums of two squares up to n^2 + n^2.
0

%I #11 Aug 18 2019 16:34:59

%S 1,2,40,4680,1591200,1891936800,4270101357600,11089453225687200,

%T 32565776278494961756800,28429922691126101613686400,

%U 42204464874461454985621846571472000

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

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

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

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

%e 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.

%o (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

%Y Cf. A069011, A001481.

%K easy,nonn

%O 0,2

%A _Carl R. White_, Jul 15 2009