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On the Partitions of a Number into Arithmetic Progressions
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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

**Abstract:**

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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