A375973 Record values in A375970.

1, 2, 5, 70, 99, 195, 240, 323, 2378, 2716, 15015, 48505, 80782, 130662, 510068, 672210, 1926615, 2744210, 4116315, 10278759, 31320850, 87347695, 93222358, 155904960, 177385520, 189539896, 250637778, 272607725, 486471832, 647562465, 1620820270

Offset: 1

Author

Robert Israel, Sep 04 2024

Keywords

• nonn

Comments

a(n) is the largest number whose square divides A000330(A375971(n)).

Examples

			a(3) = 5 because A375971(3) = 650 and 5^2 is the largest square dividing 650.
From _David A. Corneth_, Sep 13 2024: (Start)
70 is in the sequence as A000330(24) = 24 * 25 * 49 / 6 = 4 * 25 * 49. The largest square dividing 4 is 4, the largest square dividing 25 is 25 and the largest square dividing 49 is 49.
So the largest k such that k^2 divides 4 * 25 * 49 is sqrt(4)*sqrt(25)*sqrt(49) = 2*5*7 = 70, a record. (End)
		

Crossrefs

Cf. A000330, A375970, A375971.

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:
V:= NULL; m:= 0: count:= 0:
for k from 1 while count < 20 do
  v:= g(k);
  if v > m then m:= v; V:= V,v; count:= count+1; fi
od:
V;

Formula

a(n) = A375970(A375971(n)).

Extensions

a(25) from Michael S. Branicky, Sep 06 2024

a(26)-a(31) from David A. Corneth, Sep 08 2024