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 × 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 of the form p2q 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

Answer:

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