Under what conditions is the number 2ⁿ*p an abundant number? Where n is a positive integer and p is prime.

How about 3ⁿ*p?

How about 2*pⁿ?

Recall an abundant number is one whose proper factors sum to more than the number. For example 18 is abundant because 1+2+3+6+9 > 18.

(In reply to proposed solution by Charlie)

In sum: 2^n * p is abundant unless p=2 or n = 1.

Posted by Jer on 2015-10-28 11:14:06