[seqfan] Partitions of n

jnthn stdhr jstdhr at gmail.com
Sat Feb 1 18:26:10 CET 2014


Hello, seqers.

If a(n) = the number of partitions of n having all factors of n, then with
n = (1,...,inf) we get the sequence:  0,1,1,1,1,1,1,2,3,3,1,7,1,15,...

This sequence is easily  computed as follows:  Let p(n) be a partition
counting function.  Then a(n) = p( n - sum( factors of n) ).  Example:
a(10) = 3, because 10 = 2 * 5 -> 10 - (5 + 2) = 3 -> p(3) = 3 =
{(3),(2,1),(1,1,1)}, and (5,2,3), (5,2,2,1), and (5,2,1,1,1) are the only
partitions of 10 that have both 5 and 2 in them.

This sequence isn't in the database.  Is it worth adding?

Jonathan


More information about the SeqFan mailing list