Geodesic
On the partitions of a number into arithmetic progressions
Journal of integer sequences, Tome 11 (2008) no. 5
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.
Classification : 11P81, 05A15, 05A17
Keywords: partition, arithmetic progression, divisor function, Diophantine equation 
@article{JIS_2008__11_5_a6,
     author = {Munagi,  Augustine O. and Shonhiwa,  Temba},
     title = {On the partitions of a number into arithmetic progressions},
     journal = {Journal of integer sequences},
     year = {2008},
     volume = {11},
     number = {5},
     zbl = {1196.11140},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2008__11_5_a6/}
}
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Munagi,  Augustine O.; Shonhiwa,  Temba. On the partitions of a number into arithmetic progressions. Journal of integer sequences, Tome 11 (2008) no. 5. http://geodesic.mathdoc.fr/item/JIS_2008__11_5_a6/