Universal numbers

Ibrahim loves to play with numbers. He recently learned how to raise numbers to a power, and he really likes it. Farhad knows this, so he asked Ibrahim the following question: in how many different ways can one represent $n$ as the sum of three numbers with the same integer non-negative base $k$ raised to a non-negative integer.

In other words, you must find the number of different quadruples of non-negative integers ($k$, $a$, $b$, $c$), satisfying the equality n = k^a + k^b + k^c (k > 0).

Help Ibrahim to solve this problem.