Highly Abundant Numbers

December 20, 2016

We studied highly composite numbers in a series of several previous exercises, and had a lot of fun. In today’s exercise we look at a related concept: highly abundant numbers (A002093).

Highly abundant numbers are those numbers n such that sigma(m) < sigma(n) for all m < n, where m and n are positive integers and sigma(n) is the sum of the divisors of n. For instance, 12 is a highly abundant number since the sum of its divisors is 1 + 2 + 3 + 4 + 6 + 12 = 28, and no number less than 12 has a greater sum of divisors.

Your task is to compute the sequence of highly abundant numbers. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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