OFFSET
1,2
COMMENTS
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.
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).
EXAMPLE
Illustration of initial terms:
. _ _ _ _ _ _ _ _
. 1 |_| | | | | | | | | | | | | |
. 2 |_ _|_| | | | | | | | | | | |
. _ _| _|_| | | | | | | | | |
. 4 |_ _ _| _|_| | | | | | | |
. _ _ _| _| _ _| | | | | | |
. 6 |_ _ _ _| _| | | | | | |
. _ _ _ _| | | | | | | |
. 8 |_ _ _ _ _| _ _ _| | | | | |
. | _ _ _| | | | |
. _| | | | | |
. _| _| | | | |
. _ _| _| | | | |
. | _ _| | | | |
. | | _ _ _ _ _| | | |
. _ _ _ _ _ _ _ _| | | _ _ _ _ _| | |
. 16 |_ _ _ _ _ _ _ _ _| | | _ _ _ _ _ _| |
. _ _| | | _ _ _ _ _ _|
. _ _| _ _| | |
. | _| _ _| |
. _| _| | _ _|
. | _| _| |
. _ _ _| | _| _|
. | _ _ _| _ _| _|
. | | | _ _|
. | | _ _ _| |
. | | | _ _ _|
. _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | |
. 28 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | |
. | |
. | |
. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| |
. 32 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
.
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.
A317307(n) is the area (or the number of cells) in the n-th region of the diagram.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Aug 23 2018
STATUS
approved