cp's OEIS Frontend

A384230 Number of subparts in the central part of the symmetric representation of sigma(n).

%I A384230 #165 Aug 28 2025 16:44:43
%S A384230 1,1,0,1,0,2,0,1,1,0,0,2,0,0,2,1,0,3,0,2,0,0,0,2,1,0,0,2,0,4,0,1,0,0,
%T A384230 2,3,0,0,0,2,0,4,0,0,4,0,0,2,1,1,0,0,0,4,0,2,0,0,0,4,0,0,2,1,0,4,0,0,
%U A384230 0,2,0,3,0,0,0,0,2,0,0,2,1,0,0,4,0,0,0
%N A384230 Number of subparts in the central part of the symmetric representation of sigma(n).
%C A384230 This sequence shares infinitely many terms with A067742 from which first differs at a(18). It also shares with A067742 the positions of zeros and nonzeros.
%C A384230 Observation: consider the 2-dense sublists of divisors of n. At least for the first 88 terms a(n) coincides with the number of odd terms in the central 2-dense sublist of divisors of n. For more information see A384225 and A280940.
%C A384230 See the "Discussion" text file in the first link for more comments.
%H A384230 Omar E. Pol, <a href="/A384230/a384230.txt">Discussion of the Sequence A384230.</a>
%H A384230 Omar E. Pol, <a href="/A000203/a000203_1.jpg">Illustration of initial terms of A000203 in the pyramid.</a>
%H A384230 Omar E. Pol, <a href="/A001065/a001065.jpg">Illustration of initial terms of A001065 in the pyramid.</a>
%H A384230 Omar E. Pol, <a href="/A048050/a048050.jpg">Illustration of initial terms of A048050 in the pyramid.</a>
%H A384230 Omar E. Pol, <a href="/A067742/a067742.jpg">Illustration of initial terms of A067742 in the pyramid.</a>
%H A384230 Omar E. Pol, <a href="/A237593/a237593_3.png">Illustration of initial terms of A224613 (black spiders).</a>
%H A384230 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpyr02.jpg">Illustration of initial terms of A237593 (essentially a template for the Pop-Up pyramid).</a>
%H A384230 Omar E. Pol, <a href="/A221529/a221529.jpg">Prism of partitions of 10 and its companion tower (both have the same volume).</a>
%H A384230 Omar E. Pol, <a href="/A237593/a237593_1.png">The symmetric representation of sigma(n), n = 1..64 (the top view of the pyramid and of the tower).</a>
%F A384230 a(n) = 0 if and only if A067742(n) = 0.
%F A384230 a(n) >= A067742(n).
%F A384230 (a(n) - A067742(n)) is an even number.
%e A384230 See the "Discussion" text file in the first link for the examples.
%Y A384230 Cf. A001227 (number of subparts), A071561 (positions of zeros), A071562 (positions of nonzeros), A237270 (parts), A237271, A237593, A279387 (subparts), A280940, A384225, A335574, A338488, A377654.
%Y A384230 See the "Discussion" text file in the first link for more cross-references.
%K A384230 nonn,changed
%O A384230 1,6
%A A384230 _Omar E. Pol_, Jun 29 2025
%E A384230 Edited by _Omar E. Pol_, Aug 24 2025