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 A362818 #29 Aug 02 2023 14:34:27 %S A362818 4,6,8,10,8,12,8,14,14,16,8,18,8,16,20,22,8,22,8,22,24,16,8,26,18,16, %T A362818 24,28,8,30,8,30 %N A362818 Total number of edges of all polygons (or parts) of the symmetric representation of sigma(n). %C A362818 a(n) = 8 if and only if n is an odd prime. %C A362818 If the symmetric representation of sigma(n) has only one polygon (or part), or in other words, if n is a member of A174973 (also of the same sequence A238443) then a(n) = 2 + 2*(A003056(n-1) + A003056(n)). Note that A174973 = A238443 also include all powers of 2 and all even perfect numbers. %e A362818 Illustration of a(9) = 14: %e A362818 4 %e A362818 _ _ _ _ _ %e A362818 |_ _ _ _ _| %e A362818 |_ _ 6 %e A362818 |_ | %e A362818 |_|_ _ %e A362818 | | %e A362818 | | %e A362818 | | 4 %e A362818 | | %e A362818 |_| %e A362818 . %e A362818 For n = 9 the symmetric representation of sigma(9) has three parts from right to left as follows: a rectangle, a concave hexagon and a rectangle. The number of edges of the polygons are 4, 6, 4 respectively, therefore the total number of edges is 4 + 6 + 4 = 14, so a(9) = 14. %Y A362818 Row sums of A362817. %Y A362818 Cf. A000079, A000203, A000396, A003056, A065091, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A238443, A244363, A245092, A262626, A274919, A348705. %K A362818 nonn,more %O A362818 1,1 %A A362818 _Omar E. Pol_, May 04 2023