OFFSET
1,1
COMMENTS
Note that odd primes (A065091) are also the numbers j with the property that the parts of the symmetric representation of sigma(j) are two rectangles or more generally two quadrilaterals.
Conjecture 1: The octagons are S-shaped and they have width 1.
Conjecture 2: This sequence is also the primes doubled (or even semiprimes) >= 10 (Cf. A100484). - Omar E. Pol, Aug 15 2023
For the symmetric representation of sigma(n) to consist of 2 octagons the first 3 entries in row n of the triangle of A249223 must be nonzero, hence must be 1's, indicating width 1, with the remaining entries zero. Therefore, row n of A237048 is 100100..., implying n = 2*p with p>3 prime. Both conjectures are true. - Hartmut F. W. Hoft, Aug 22 2023
From Omar E. Pol, Aug 23 2023: (Start)
Also the row numbers of the triangle A364639 where the rows are [1, 0, -1, 1] or where the rows start with [1, 0, -1, 1] and the remaining terms are zeros.
EXAMPLE
The symmetric representation of sigma(14) in the first quadrant is as follows:
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The diagram has only two parts (or polygons) and both are octagons so 14 is in the sequence.
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, May 06 2023
EXTENSIONS
More terms from Omar E. Pol, Aug 15 2023
STATUS
approved