Problem:

Caboyara, a famous Australian circus performer, once again this year performs a great trick. He sets up a spectacular staircase with $N = p_{1} \cdot p_{2} \cdot \ldots \cdot p_{2015}$ steps, where $p_{1}, p_{2}, \ldots, p_{2015}$ are distinct prime numbers; the steps corresponding to divisors of $N$ (including the first and the $N$-th step) are special and are initially lit up green.
During the show, 2015 trained kangaroos climb the staircase one after another; for $i = 1, 2, \ldots, 2015$, the $i$-th kangaroo jumps $p_{i}$ steps at a time, starting from the foot of the staircase (it jumps onto step $p_{i}$, then onto $2 p_{i}$, and so on until it reaches step $N$). Every time a kangaroo jumps onto a special step, it changes color: from green it becomes red, from red it becomes green.
How many special steps will be lit up green at the end of the performance?