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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.

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A362818 Total number of edges of all polygons (or parts) of the symmetric representation of sigma(n).

Original entry on oeis.org

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, 24, 28, 8, 30, 8, 30
Offset: 1

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Author

Omar E. Pol, May 04 2023

Keywords

Comments

a(n) = 8 if and only if n is an odd prime.
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.

Examples

			Illustration of a(9) = 14:
         4
     _ _ _ _ _
    |_ _ _ _ _|
              |_ _ 6
              |_  |
                |_|_ _
                    | |
                    | |
                    | |  4
                    | |
                    |_|
.
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.

Crossrefs

Row sums of A362817.
Cf. A000079, A000203, A000396, A003056, A065091, A174973, A196020, A235791, A236104, A237270, A237271, A237591, A237593, A238443, A244363, A245092, A262626, A274919, A348705.
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