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
Keywords
Examples
a(12) = 5 because A000330(12) = 650 = 2 * 5^2 = 13 and 5^2 is the largest square dividing 650.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
-
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]);
-
PARI
a(n) = my(m=n*(n+1)*(2*n+1)/6); sqrtint(m/core(m)); \\ Michel Marcus, Sep 06 2024
Comments