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

1,1

Comments

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

Links

Table of n, a(n) for n=1..39.

Example

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.

Mathematica

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

Crossrefs

Intersection of A000217 and A068088.

Cf. A005117.

Sequence in context: A025754 A071128 A065782 * A160482 A135626 A064566

Adjacent sequences: A374390 A374391 A374392 * A374394 A374395 A374396

Keyword

nonn

Author

Massimo Kofler, Jul 07 2024

Status

approved