IBM Ponder This #266 · June 2020

This is the 278th Ponder This monthly challenge. If you sum the divisors of 278 (excluding itself), you get 142, which is the number of challenges I wrote for IBM's puzzle corner. There are 138 natural numbers that are smaller than 278 and relatively prime to it. 138 is also the number of challenges our best solver to date, Daniel Bitin, has correctly solved.

It was an honor serving as IBM research's PuzzleMaster for more than a decade. As I'm leaving IBM, I welcome Gadi Aleksandrowicz, our new PuzzleMaster, and devote this month's challenge to him.

Your challenge is to find a number whose sum of divisors (excluding itself) is 12,142,680,281,284,711,468,101,282,998,309,016,699,980,172 and exactly 3,031,634,148,236,289,733,373,855,928,919,180,891,127,808 out of the natural numbers that are smaller than it are relatively prime to it.

A bonus '*' for finding the connection to Gadi.

Solution

Best opened after a real attempt

To be added.