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A362818
Total number of edges of all polygons (or parts) of the symmetric representation of sigma(n).
1
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
1,1
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.
EXAMPLE
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.
KEYWORD
nonn,more
AUTHOR
Omar E. Pol, May 04 2023
STATUS
approved