polite number


A polite number n is an integer that is the sum of two or more consecutive nonnegative integers in at least one way. To put it algebraically, if n is polite then there is a solution to

n=i=abi

with b>a and a>-1. For example, 42 is a polite number since it is the sum of the integers from 3 to 9. The first few polite numbers are 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, etc.

Obviously all triangular numbersMathworldPlanetmath are polite numbers. So are all odd numbersMathworldPlanetmathPlanetmath. In fact, the numbers that are not polite are the powers of 2.

Title polite number
Canonical name PoliteNumber
Date of creation 2013-03-22 18:09:54
Last modified on 2013-03-22 18:09:54
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 6
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A25