A374393 Triangular numbers such that the three numbers before it and the three numbers after it are squarefree.

36, 2016, 2556, 3240, 9180, 10296, 23220, 23436, 25200, 39060, 41616, 67896, 93096, 97020, 122760, 126756, 170820, 215496, 253116, 313236, 320400, 365940, 437580, 438516, 446040, 499500, 508536, 574056, 592416, 653796, 673380, 738720, 749700, 839160, 850860, 924120, 936396, 1024596, 1036080

Offset: 1

Author

Massimo Kofler, Jul 07 2024

Keywords

• nonn

Comments

All terms of this sequence are divisible by 36, so they can't be squarefree.

Examples

			36 = 2^2 * 3^2 (the 8th triangular number) between 33 = 3 * 11, 34 = 2 * 17, 35 = 5 * 7 and 37 which is a prime number, 38 = 2 * 19 and 39 = 3 * 13.
2016 = 2^5 * 3^2 * 7 (the 63rd triangular number) between 2013 = 3 * 11 * 61, 2014 = 2 * 19 * 53, 2015 = 5 * 13 * 31 and 2017 which is a prime number, 2018 = 2 * 1009, 2019 = 3 * 673.
2556 = 2^2 * 3^2 * 71 (the 71st triangular number) between 2553 = 3 * 23 * 37, 2554 = 2 * 1277, 2555 = 5 * 7 * 73 and 2557 which is a prime number, 2558 = 2 * 1279, 2559 = 3 * 853.
		

Crossrefs

Intersection of A000217 and A068088.

Cf. A005117.

Programs

Mathematica

Select[Accumulate[Range[1500]], And @@ (SquareFreeQ /@ (# + {-3, -2, -1, 1, 2, 3})) &] (* Amiram Eldar, Jul 07 2024 *)