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

1,2

Comments

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

Links

Table of n, a(n) for n=1..31.

Formula

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

Example

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)

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;

Crossrefs

Cf. A000330, A375970, A375971.

Sequence in context: A133004 A321602 A175169 * A066933 A132496 A100009

Adjacent sequences: A375970 A375971 A375972 * A375974 A375975 A375976

Keyword

nonn

Author

Robert Israel, Sep 04 2024

Extensions

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

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

Status

approved