OFFSET
1,1
COMMENTS
All terms of this sequence are divisible by 4, so they can't be squarefree.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
36 = 2^2 * 3^2 (the 8th triangular number) between 34 = 2 * 17, 35 = 5 * 7 and 37 which is a prime number, 38 = 2 * 19.
300 = 2^2 * 3 * 5^2 (the 24th triangular number) between 298 = 2 * 149, 299 = 13 * 23 and 301 = 7 * 43, 302 = 2 * 151.
780 = 2^2 * 3 * 5 * 13 (the 39th triangular number) between 778 = 2 * 389, 779 = 19 * 41 and 781 = 11 * 71, 782 = 2 * 17 * 23.
MAPLE
select(t -> andmap(numtheory:-issqrfree, [t-2, t-1, t+1, t+2]), [seq(seq((8*t+i)*(8*t+i+1)/2, i=[-1, 0]), t=1..100)]); # Robert Israel, Jan 31 2025
MATHEMATICA
Select[Accumulate[Range[400]], And @@ (SquareFreeQ /@ (# + {-2, -1, 1, 2})) &] (* Amiram Eldar, Jul 09 2024 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Massimo Kofler, Jul 09 2024
STATUS
approved