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A175239
Number of AP divisors of n.
0
1, 2, 3, 3, 3, 4, 3, 4, 4, 5, 3, 6, 3, 5, 5, 5, 3, 7, 3, 6, 6, 5, 3, 8, 4, 5, 6, 6, 3, 9, 3, 6, 6, 5, 5, 10, 3, 5, 6, 8, 3, 9, 3, 7, 8, 5, 3, 10, 4, 7, 6, 7, 3, 9, 6, 8, 6, 5, 3, 13, 3, 5, 8, 7, 6, 9, 3, 7, 6, 9, 3, 12, 3, 5, 9, 7, 5, 10, 3, 10, 7, 5, 3, 13, 6, 5, 6, 8, 3, 14, 5, 7, 6, 5, 6, 12, 3, 7, 8, 10
OFFSET
1,2
COMMENTS
The following definition is given in the reference: k is an AP divisor of n if there exists a partition of n that is an arithmetic progression of length k; arithmetic progressions of length 1 or greater are counted.
Terms 1-30 were given in the reference; others were calculated from the generating function by the author.
LINKS
Augustine O. Munagi, Combinatorics of Integer Partitions in Arithmetic Progression, Integers, A7, Volume 10 (2010), 73-82.
FORMULA
G.f.: sum(k>=1, q^k*(1+q^k+q^(2*k^2))/(1-q^(2*k)) ).
EXAMPLE
The partitions of 4 that are arithmetic progressions are (4), (2,2), (3,1) and (1,1,1,1) with lengths 1, 2, 2 and 4, respectively. The AP divisors of 4 are thus 1, 2 and 4, so a(4)=3. - Corrected by Jaroslav Krizek, Mar 26 2010
CROSSREFS
Sequence in context: A322988 A098201 A341883 * A176228 A322822 A305232
KEYWORD
nonn
AUTHOR
John W. Layman, Mar 10 2010
STATUS
approved