  The image of Euler's totient function is composed of the number 1 and even
numbers. However, many even numbers are not in the image. We consider the
problem of finding those even numbers which are in the image and those which
are not. If an even number is in the image, then its preimage can have at most
half its elements odd. However, it may contain only even numbers. We consider
the structure of the preimage of certain numbers in the image of the totient
function.
