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From the article Number Theory in the 1994 Microsoft Encarta: "If a, b, c are integers such that a = bc, a is called a multiple of b or of c, and b or c is called a divisor or factor of a. If c is not 1, b is called a proper divisor of a. Even integers, which include 0, are multiples of 2, for example, -4, 0, 2, 10; an odd integer is an integer that is not even, for example, -5, 1, 3, 9. A perfect number is a positive integer that is equal to the sum of all its positive, proper divisors; for example, 6, which equals 1 + 2 + 3, and 28, which equals 1 + 2 + 4 + 7 + 14, are perfect numbers. A positive number that is not perfect is imperfect and is deficient or abundant according to whether the sum of its positive, proper divisors is smaller or larger than the number itself. Thus, 9, with proper divisors 1, 3, is deficient; 12, with proper divisors 1, 2, 3, 4, 6, is abundant."
Problem Statement: Given a number, determine if it is perfect, abundant, or deficient.
A list of N positive integers (none greater than 60,000), with 1 < N < 100. A 0 will mark the end of the list.
The N lines of output should list for each input integer whether it is perfect, deficient, or abundant, as shown in the example below.
15 28 6 56 60000 22 496 0
15 DEFICIENT 28 PERFECT 6 PERFECT 56 ABUNDANT 60000 ABUNDANT 22 DEFICIENT 496 PERFECT