Question

The proper factors of a number n are the factors which are less than n.
A number n is deficient if the sum of its proper factors is less than n. For example, 22 is deficient since 1 + 2 + 11 = 14 < 22
A number n is super-deficient if twice the sum of its proper factors is less than n. For example, all odd primes p are super-deficient since 2 x 1 = 2 < p.
A.) Find the two smallest super-deficient odd composite numbers that are not squares.
B.) Explain why no even number is super-deficient.
C.) Find the smallest super-deficient number in the form of p^2q where p and q are different primes.
D.) A number n = pq, where p and q are different odd primes, is not super-deficient. Find all possible values for n. Show that there are no more.

Answer 1

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Answer 2

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