A362817 Irregular triangle read by rows: T(n,k) (n>=1, k>=1) is the number of edges of the k-th polygon (or part), from left to right, of the symmetric representation of sigma(n).

4, 6, 4, 4, 10, 4, 4, 12, 4, 4, 14, 4, 6, 4, 8, 8, 4, 4, 18, 4, 4, 8, 8, 4, 12, 4, 22, 4, 4, 22, 4, 4, 22, 4, 8, 8, 4, 8, 8, 4, 4, 26, 4, 10, 4, 8, 8, 4, 8, 8, 4, 28, 4, 4, 30, 4, 4, 30

Offset: 1

Author

Omar E. Pol, May 04 2023

Keywords

• nonn
• tabf
• more

Comments

Row n is [4, 4] 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 row n has only a term: T(n,1) = 2 + 2*(A003056(n-1) + A003056(n)). Note that A174973 = A238443 also include all powers of 2 and all even perfect numbers.

Examples

			Triangle begins:
   4;
   6;
   4,  4;
  10;
   4,  4;
  12;
   4,  4;
  14;
   4,  6,  4;
   8,  8;
   4,  4;
  18;
   4,  4;
   8,  8;
   4, 12,  4;
  ...
Illustration of row 9:
         4
     _ _ _ _ _
    |_ _ _ _ _|
              |_ _ 6
              |_  |
                |_|_ _
                    | |
                    | |
                    | |  4
                    | |
                    |_|
.
For n = 9 the symmetric representation of sigma(9) has three parts from left to right as follows: a rectangle, a concave hexagon and a rectangle. The number of edges of the polygons are 4, 6, 4 respectively, so the row 9 of the triangle is [4, 6, 4].
		

Crossrefs

Row lengths give A237271.

Row sums give A362818.

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