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 A255346 #14 Jul 31 2025 09:35:23
%S A255346 14,20,21,33,34,35,38,39,44,45,50,51,54,55,56,57,62,65,68,69,74,75,76,
%T A255346 77,84,85,86,87,90,91,92,93,94,95,98,99,104,105,110,111,114,115,116,
%U A255346 117,118,119,122,123,129,132,133,134,135,140,141,142,143,144,145,146,147,152,153,154
%N A255346 Numbers k such that k and k+1 both have at least two distinct prime factors.
%C A255346 These numbers provide solutions to the problem of finding (x,y) such that x(x+1) | y(y+1) but none of x or x+1 divides any of y or y+1. Namely, these solutions are given for (x,y) being members of the sequence such that x(x+1) divides y(y+1), the smallest of which are (14,20), (14,35), (20,35), ... but, e.g., (14,69) is excluded since 14 | 70.
%C A255346 Contains A074851 as a subsequence.
%H A255346 Harvey P. Dale, <a href="/A255346/b255346.txt">Table of n, a(n) for n = 1..1000</a>
%H A255346 T. Korimort, <a href="https://www.linkedin.com/groups/Let-x-y-be-positive-4510047.S.5973962079390941188">How many (x,y) satisfy x(x+1)|y(y+1),...</a>, Number Theory group on LinkedIn.com, Feb. 2014.
%t A255346 SequencePosition[Table[If[PrimeNu[n]>1,1,0],{n,200}],{1,1}][[;;,1]] (* _Harvey P. Dale_, Jul 30 2025 *)
%o A255346 (PARI) for(n=2,199,omega(n)>=2||(n++&&next);omega(n-1)>=2&&print1((n-1)","))
%Y A255346 Cf. A074851.
%K A255346 nonn,easy
%O A255346 1,1
%A A255346 _M. F. Hasler_, Feb 21 2015