If n is an odd integer, show that $\displaystyle \phi(2n) = \phi(n)$.

I know this is true, but I'm having difficulties showing that n is odd without getting into n=2k+1 troubles. I know that to make n even, you can have $\displaystyle n=2^kj$ for some gcd(2,j) = 1, that way all your 2s are separated, but other than that - how do you show its even?

Should I write the prime factorization of n? where none equal 2?