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
KEYWORD
nonn
AUTHOR
John W. Layman, Mar 10 2010
STATUS
approved