Journal of Integer Sequences, Vol. 11 (2008), Article 08.5.4

On the Partitions of a Number into Arithmetic Progressions

Augustine O. Munagi and Temba Shonhiwa
The John Knopfmacher Centre for Applicable Analysis and Number Theory
School of Mathematics
University of the Witwatersrand
Private Bag 3, Wits 2050
South Africa


The paper investigates the enumeration of the set AP(n) of partitions of a positive integer n in which the nondecreasing sequence of parts form an arithmetic progression. We establish formulas for such partitions, and characterize a class of integers n with the property that the length of every member of AP(n) divides n. We prove that the number of such integers is small.

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(Concerned with sequences A004119 A035250 and A049988.)

Received October 8 2007; revised version received October 10 2007; December 5 2008. Published in Journal of Integer Sequences, December 13 2008.

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