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(This article was first published on Revolutions, and kindly contributed to R-bloggers) by Seth Mottaghinejad Let's review the Collatz conjecture, which says that given a positive integer n, the following recursive algorithm will always terminate:...

Inspired by our Open Season post on the Perfect Cuboid earlier this year, Aperiodical reader Jos Schouten wrote to us describing his work on the problem over the past 20 years. He’s looking for someone to help take his work further. Are you up...

I know of no practical use for Amicable numbers, but they’re rather fun. And rare. But let’s start with a definition. Let be a natural number (a positive integer), and let with and , be the sum of the divisors of . We’re in fact interested...

I have solved a question that says: Given a natural number n (1 <= n <= 500000), please output the summation of all its proper divisors. Definition: A proper divisor of a natural number is the divisor that is strictly less than the number. e...

I'm learning algorithmic programming in Java. I wrote an algorithm for the following problem: Given a natural number n (1 <= n <= 500000), please output the summation of all its proper divisors. Definition: A proper divisor of a natural number...