Problem 2595. Polite numbers. Politeness.

Created by Jan Orwat
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A polite number is an integer that sums of two or more consecutive positive integers. Politeness of a positive integer is a number of nontrivial ways to write n as a sum of two or more consecutive positive integers.

For example 9 = 4+5 = 2+3+4 and politeness of 9 is 2.

Given N return politeness of N.

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Last Solution submitted on Dec 03, 2024

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John D'Errico on 21 Aug 2016

An interesting problem, enough so that I chose to solve it in three essentially different ways. As always, there are various ways to solve any problem. The first two ways were essentially constructive, so counting the set of solutions for any N. The last used a formulaic approach.

Rafael S.T. Vieira on 11 Aug 2020

Politeness is an integer sequence defined at https://oeis.org/A069283.

goc3 on 13 Jan 2021

@Dyuman Joshi: I do not know why that error occurs. I do know that it essentially means that the user needs to wait and re-submit their solution at a later time, sometimes the next day.

By the way, it's best to not post solutions (or solution attempts) in comments. Questions or comments specific to a solution can be posted in a comment tied to said solution or solution attempt.

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