A375970 - OEIS

%I #13 Sep 06 2024 20:16:22

%S 1,1,1,1,1,1,2,2,1,1,1,5,3,1,2,2,1,1,1,1,1,1,2,70,5,3,3,1,1,1,4,4,1,1,

%T 1,1,5,1,2,6,1,1,1,1,1,1,2,14,35,5,1,1,3,3,2,2,1,1,1,11,1,5,4,4,1,1,3,

%U 1,1,1,2,2,7,5,5,1,1,1,2,6,3,1,1,13,1,1,10,2,1,1,1,1,1,3,4,4,7

%N a(n) is the largest number k such that k^2 divides the square pyramidal number A000330(n).

%C a(n)^2 is the largest square that divides n*(n+1)*(2*n+1)/6.

%H Robert Israel, <a href="/A375970/b375970.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000188(A000330(n)).

%e a(12) = 5 because A000330(12) = 650 = 2 * 5^2 = 13 and 5^2 is the largest square dividing 650.

%p g:= proc(n) local t,s,F; t:= n*(n+1)*(2*n+1)/6;

%p   F:= ifactors(t)[2];

%p   mul(s[1]^floor(s[2]/2), s=F)

%p end proc:

%p map(g, [$1..100]);

%o (PARI) a(n) = my(m=n*(n+1)*(2*n+1)/6); sqrtint(m/core(m)); \\ _Michel Marcus_, Sep 06 2024

%Y Cf. A000188, A000330, A119356, A375971, A375973.

%K nonn

%O 1,7

%A _Robert Israel_, Sep 04 2024