This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A374393 #6 Jul 25 2024 23:04:08
%S A374393 36,2016,2556,3240,9180,10296,23220,23436,25200,39060,41616,67896,
%T A374393 93096,97020,122760,126756,170820,215496,253116,313236,320400,365940,
%U A374393 437580,438516,446040,499500,508536,574056,592416,653796,673380,738720,749700,839160,850860,924120,936396,1024596,1036080
%N A374393 Triangular numbers such that the three numbers before it and the three numbers after it are squarefree.
%C A374393 All terms of this sequence are divisible by 36, so they can't be squarefree.
%e A374393 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.
%e A374393 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.
%e A374393 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.
%t A374393 Select[Accumulate[Range[1500]], And @@ (SquareFreeQ /@ (# + {-3, -2, -1, 1, 2, 3})) &] (* _Amiram Eldar_, Jul 07 2024 *)
%Y A374393 Intersection of A000217 and A068088.
%Y A374393 Cf. A005117.
%K A374393 nonn
%O A374393 1,1
%A A374393 _Massimo Kofler_, Jul 07 2024