Identities involving sum of divisors, compositions and integer partitions hiding in the q-binomial theorem

In this paper we show some identities come from the q-binomial theorem and the triple product of Jacobi. Some of these identities relating the function sum of divisor of a positive integer n and the number of integer partitions of n. As corollary we found the next equation, for n >= 1. Sigma(n)(l=1) k(l)/l! Sigma((w1, w2, ... , wl)is an element of Cn) sigma(1)(w(1))sigma(1)(w(2)) ... sigma(1)(w(l))/w(1)w(2) ... w(l) = p(k)(n), where sigma(1)(n) is the sum of all positive divisors of n, p(k)(n) is the number of k-colored integer partitions of n, and C-n is the set of integer compositions of n.