Abstract :
Let φ(x) be Euler′s totient function. If the equation φ(x) = n has no solution, then n is called a nontotient. In this paper, we prove that a nontotient can have an arbitrary divisor and we give two sorts of odd numbers such that for the odd number k of the first sort, 2α · k is a nontotient for a given positive integer α while for the odd number k of the second sort, 2α · k is a nontotient for arbitrary positive integer α.
