## Polygon Numbers Associated with the Sum of Odd Divisors Function

2016-08-22T18:04:37Z (GMT)
by

Let *n* be a positive integer. We investigate the sequences ((*S _{m}*(

*n*))

_{m}, which concerns the iteration of the odd divisor function

*S*, given by In this article, we introduced and studied the following invariants:

*order,*For

*m*-gonal shape number, type, convexity, and area of*n*derived from*S*(_{m}*n*).*m*= 3, 4, 5, we classify

*m*-gonal shape odd prime integers. According to some numerical computational evidence in the Appendix (see supplemental data), we state conjectures and questions with respect to the existence problem for

*m*-gonal shape numbers. An inductive algorithm for finding

*m*+ 1-gonal shape prime integers when an

*m*-gonal shape integer is given. We give some examples and illustrations, for our conjectures and questions.