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Some questions of abundance (Posted on 2015-10-28) Difficulty: 2 of 5
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.

No Solution Yet Submitted by Jer    
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re: proposed solution / counterexample | Comment 2 of 3 |
(In reply to proposed solution by Charlie)

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


p=7, n=2 yields 28 which is perfect, not abundant

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