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

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, 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, 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

Offset

1,7

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

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

Example

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

Maple

g:= proc(n) local t, s, F; t:= n*(n+1)*(2*n+1)/6;
  F:= ifactors(t)[2];
  mul(s[1]^floor(s[2]/2), s=F)
end proc:
map(g, [$1..100]);

Prog

(PARI) a(n) = my(m=n*(n+1)*(2*n+1)/6); sqrtint(m/core(m)); \\ Michel Marcus, Sep 06 2024

Crossrefs

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

Sequence in context: A180264 A225200 A128706 * A253586 A347621 A318191

Adjacent sequences: A375967 A375968 A375969 * A375971 A375972 A375973

Keyword

nonn

Author

Robert Israel, Sep 04 2024

Status

approved