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 A386993 #18 Aug 30 2025 15:56:32 %S A386993 1,1,2,2,1,2,2,2,2,2,3,2,2,4,2,2,2,2,1,2,4,2,3,2,2,4,2,1,2,2,2,4,2,4, %T A386993 4,2,2,2,2,4,1,2,4,3,2,2,2,3,2,2,2,2,4,2,4,2,3,4,2,4,2,2,2,2,4,2,2,2, %U A386993 3,4,2,2,4,2,4,2,4,2,4,3,2,4,2,2,2,2,4,2,3,4,2,2,2,3,4,2,2,4,4,2,5,2,2,3,2 %N A386993 Number of 2-dense sublists of divisors of the n-th squarefree number. %C A386993 In a sublist of divisors of k the terms are in increasing order and two adjacent terms are the same two adjacent terms in the list of divisors of k. %C A386993 The 2-dense sublists of divisors of k are the maximal sublists whose terms increase by a factor of at most 2. %H A386993 Paolo Xausa, <a href="/A386993/b386993.txt">Table of n, a(n) for n = 1..10000</a> %F A386993 a(n) = A237271(A005117(n)). (conjectured). %e A386993 For n = 11 the 11th squarefree number is 15. The list of divisors of 15 is [1, 3, 5, 15]. There are three 2-dense sublists of divisors of 15, they are [1], [3, 5], [15], so a(11) = 3. %t A386993 Map[Length[Split[Divisors[#], #2 <= 2*# &]] &, Select[Range[150], SquareFreeQ]] (* _Paolo Xausa_, Aug 29 2025 *) %Y A386993 Cf. A005117, A174973 (2-dense numbers), A237271, A379288, A380328, A384149, A384222, A384225, A384226, A384928, A384930, A384931, A386984, A386992, A387030. %K A386993 nonn,new %O A386993 1,3 %A A386993 _Omar E. Pol_, Aug 23 2025