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A375970 a(n) is the largest number k such that k^2 divides the square pyramidal number A000330(n).

%I A375970 #13 Sep 06 2024 20:16:22
%S A375970 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 A375970 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 A375970 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 A375970 a(n) is the largest number k such that k^2 divides the square pyramidal number A000330(n).
%C A375970 a(n)^2 is the largest square that divides n*(n+1)*(2*n+1)/6.
%H A375970 Robert Israel, <a href="/A375970/b375970.txt">Table of n, a(n) for n = 1..10000</a>
%F A375970 a(n) = A000188(A000330(n)).
%e A375970 a(12) = 5 because A000330(12) = 650 = 2 * 5^2 = 13 and 5^2 is the largest square dividing 650.
%p A375970 g:= proc(n) local t,s,F; t:= n*(n+1)*(2*n+1)/6;
%p A375970   F:= ifactors(t)[2];
%p A375970   mul(s[1]^floor(s[2]/2), s=F)
%p A375970 end proc:
%p A375970 map(g, [$1..100]);
%o A375970 (PARI) a(n) = my(m=n*(n+1)*(2*n+1)/6); sqrtint(m/core(m)); \\ _Michel Marcus_, Sep 06 2024
%Y A375970 Cf. A000188, A000330, A119356, A375971, A375973.
%K A375970 nonn
%O A375970 1,7
%A A375970 _Robert Israel_, Sep 04 2024