A unitary divisor of a number n is a number d such that d|n and gcd(d, n/d)=1. For example, 3 is a unitary divisor of 12 because gcd(3, 12/3)=gcd(3, 4)=1.

A unitary perfect number is a number that is the sum of its unitary divisors less than itself. For example, 60 is a unitary perfect number because its unitary divisors less than itself are 1, 3, 4, 5, 12, 15, and 20, and 1+3+4+5+12+15+20=60. Find all unitary perfect numbers less than 1000000.

(In reply to just look up - spoiler by Ady TZIDON)

For what it's worth, 146361946186458562560000 is 2^18 * 3 * 5^4 * 7 * 11 * 13 * 19 * 37 * 79 * 109 * 157 * 313. As this represents 12 unique primes, it has 2^12 - 1 = 4095 unitary factors less than itself.

Corrected per Ady's later comment.

Edited on December 17, 2013, 10:06 am

Posted by Charlie on 2013-12-16 16:41:29