p^x is an infinitary divisor of p^y (with y>0) if p^x |_(y - 1) p^y, where d|_k n denotes a k-ary Divisor. Infinitary divisors therefore generalize the concept of the k-ary divisor. Infinitary divisors can also be defined as follows. Compute the prime factorization for each divisor d of n, d = product_(i = 1)^k p_i^(α_i).

divisor | infinitary perfect number | k-ary divisor | unitary divisor