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 A386984 #23 Aug 29 2025 11:08:54 %S A386984 1,1,1,3,1,3,1,3,1,5,3,5,1,5,1,5,1,5,1,3,1,7,3,3,1,5,3,7,1,5,1,3,1,7, %T A386984 3,5,1,3,1,5,1,7,1,7,1,5,3,5,1,5,1,7,3,5,1,7,1,7,5,7,1,5,3,3,1,7,1,7, %U A386984 1,7,5,5,1,7,1,7,3,5,1,3,1,9,3,7,1,7,1,7,1,5,1,5,1,9,3,3,1,3,1,9,1 %N A386984 Number of 2-dense sublists of divisors of the n-th hexagonal number. %C A386984 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 A386984 The 2-dense sublists of divisors of k are the maximal sublists whose terms increase by a factor of at most 2. %C A386984 Conjecture: all terms are odd. %H A386984 Paolo Xausa, <a href="/A386984/b386984.txt">Table of n, a(n) for n = 0..10000</a> %F A386984 a(n) = A237271(A000384(n)) for n >= 1 (conjectured). %e A386984 For n = 3 the third positive hexagonal 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(3) = 3. %t A386984 A386984[n_] := Length[Split[Divisors[PolygonalNumber[6, n]], #2 <= 2*# &]]; %t A386984 Array[A386984, 100, 0] (* _Paolo Xausa_, Aug 29 2025 *) %Y A386984 Bisection of A384928. %Y A386984 Cf. A000384, A174973 (2-dense numbers), A237271, A379288, A384149, A384222, A384225, A384226, A384930, A384931, A386989. %K A386984 nonn,changed %O A386984 0,4 %A A386984 _Omar E. Pol_, Aug 11 2025