some hints:
use pascal triangle to generate c(n,k) if you use 63 bits data type all will fit.
prime factorize each number
for each prime count the number of number where he is a factor
calculate number of posibilites
remove duplicates ( this is what makes this problem a little bit harder ).

Good luck.

If you don't know how to do this part take a look at derivation of Euler's totient function.