A partition of the positive integer n is obtained by writing

where n₁, n₂,…, n_k are positive integers, and the order in which n₁, n₂,…, n_k appear is unimportant. The number of partitions of n is denoted by p(n). For example, the partitions of 5 are

and hence p(5) =  7. The values of p(n) for small values of n are as follows:

Table of values of p(n)

The asymptotic approximation (see asymptotically equal)

for large n, was famously obtained by Hardy and Ramanujan in 1918.

Compare composition (of a number).