A374503 Positive triangular numbers such that the two numbers before it and the two numbers after it are squarefree.

36, 300, 780, 1596, 2016, 2556, 2628, 3240, 3828, 4560, 5460, 6216, 7260, 8256, 9180, 10296, 10440, 11628, 12720, 14196, 16836, 18336, 18528, 21528, 23220, 23436, 25200, 26796, 28680, 32640, 34716, 34980, 37128, 39060, 41616, 43956, 46056, 48516, 48828, 51360, 53628, 56280, 64980, 67896, 70500

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

Cf. A000217, A005117.

Sequence in context: A226836 A218647 A067741 * A185096 A073972 A219633

Adjacent sequences: A374500 A374501 A374502 * A374504 A374505 A374506

Keyword

nonn

Author

Massimo Kofler, Jul 09 2024

Status

approved