The function p(n) represents the number of distinct ways to express the integer n as a sum of positive integers, disregarding the order of the summands. For example, p(4) = 5 because the integer 4 can be expressed as 4 , 3+1 , 2+2 , 2+1+1 , and 1+1+1+1 . The study of p(n) is a part of number theory and has connections to combinatorics and partition theory. The function grows rapidly as n increases, and various formulas and approximations, such as Euler's formula, have been developed to calculate p(n) efficiently.