Variation on euler totient/phi function Is there any efficient way , to find for a particular n, the cardinality of set consisting of all numbers coprimes to n, but bigger than m(assuming i know the prime factorisation of n and m)
I am looking for the implementation which is simple+fast (like the euler totient/phi function, which given the factorisation of n will just need O(logn) steps). 

You variation seems to have 2 parameters, $n$ and $m$, but no matter - for any $n$, {\em all} primes, except the (finite) set of prime factors, are coprime to any number $n$ (except itself), so the set of those primes $\ge m$ will still be infinite.
