## Conjecture on a Relation Between Smaller Numbers of Amicable Pairs and Poulet Numbers Divisible by 5

**Authors:** Marius Coman

In a previous paper I presented seven sequences of numbers of the form 2*k*P – (30 + 290*n)*k – 315, where P is Poulet number, and I conjectured that two of them have all the terms odd abundant numbers and the other five have an infinity of terms odd abundant numbers. Because it is known that all the smaller numbers of amicable pairs are abundant numbers (see A002025 in OEIS), in this paper I revert the relation from above and I conjecture that all Poulet numbers P divisible by 5 can be written as P = (A + 315 + (30 + 290*n)*k)/(2*k), where A is a smaller of an amicable pair and n and k naturals. For example: 645 = (12285 + 315 + 30*10)/(2*10); also 1105 = (12285 + 315 + 2060*84)/(2*84) or 1105 = (69615 + 315 + 320*37)/(2*37). Note that for the first 17 such Poulet numbers there exist at least a combination [n, k] for A = 12285, the first smaller of an amicable pair divisible by 5!

**Comments:** 3 Pages.

**Download:** **PDF**

### Submission history

[v1] 2018-01-24 11:27:10

**Unique-IP document downloads:** 4 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*