OFFSET
1,1
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.
EXAMPLE
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
KEYWORD
nonn,tabf,more
AUTHOR
Omar E. Pol, May 04 2023
STATUS
approved