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 A317306 #42 Sep 30 2023 15:15:07 %S A317306 1,2,4,6,8,16,28,32,64,128,256,496,512,1024,2048,4096,8128,8192,16384, %T A317306 32768,65536,131072,262144,524288,1048576,2097152,4194304,8388608, %U A317306 16777216,33550336,33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296,8589869056,8589934592 %N A317306 Powers of 2 and even perfect numbers. %C A317306 Numbers k such that the symmetric representation of sigma(k) has only one part, and apart from the central width, the rest of the widths are 1's. %C A317306 Note that the above definition implies that the central width of the symmetric representation of sigma(k) is 1 or 2. For powers of 2 the central width is 1. For even perfect numbers the central width is 2 (see example). %e A317306 Illustration of initial terms: %e A317306 . _ _ _ _ _ _ _ _ %e A317306 . 1 |_| | | | | | | | | | | | | | %e A317306 . 2 |_ _|_| | | | | | | | | | | | %e A317306 . _ _| _|_| | | | | | | | | | %e A317306 . 4 |_ _ _| _|_| | | | | | | | %e A317306 . _ _ _| _| _ _| | | | | | | %e A317306 . 6 |_ _ _ _| _| | | | | | | %e A317306 . _ _ _ _| | | | | | | | %e A317306 . 8 |_ _ _ _ _| _ _ _| | | | | | %e A317306 . | _ _ _| | | | | %e A317306 . _| | | | | | %e A317306 . _| _| | | | | %e A317306 . _ _| _| | | | | %e A317306 . | _ _| | | | | %e A317306 . | | _ _ _ _ _| | | | %e A317306 . _ _ _ _ _ _ _ _| | | _ _ _ _ _| | | %e A317306 . 16 |_ _ _ _ _ _ _ _ _| | | _ _ _ _ _ _| | %e A317306 . _ _| | | _ _ _ _ _ _| %e A317306 . _ _| _ _| | | %e A317306 . | _| _ _| | %e A317306 . _| _| | _ _| %e A317306 . | _| _| | %e A317306 . _ _ _| | _| _| %e A317306 . | _ _ _| _ _| _| %e A317306 . | | | _ _| %e A317306 . | | _ _ _| | %e A317306 . | | | _ _ _| %e A317306 . _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | %e A317306 . 28 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | %e A317306 . | | %e A317306 . | | %e A317306 . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | %e A317306 . 32 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| %e A317306 . %e A317306 The diagram shows the first eight terms of the sequence. The symmetric representation of sigma has only one part, and apart from the central width, the rest of the widths are 1's. %e A317306 A317307(n) is the area (or the number of cells) in the n-th region of the diagram. %Y A317306 Union of A000079 and A000396 assuming there are no odd perfect numbers. %Y A317306 Subsequence of A174973. %Y A317306 Cf. A249351 (the widths). %Y A317306 Cf. A317307(n) = sigma(a(n)). %Y A317306 Cf. A000203, A000225, A139256, A196020, A236104, A235791, A237048, A237591, A237593, A237270, A237271, A239660, A239931, A239932, A239933, A239934, A244050, A245092, A262626. %K A317306 nonn,easy %O A317306 1,2 %A A317306 _Omar E. Pol_, Aug 23 2018