[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
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