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Unitary perfect numbers (Posted on 2013-12-16) Difficulty: 3 of 5
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.

See The Solution Submitted by Math Man    
Rating: 5.0000 (1 votes)

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Some Thoughts re(2): just look up by SH | Comment 7 of 10 |
(In reply to re: just look up - spoiler by Steve Herman)

1.       Nothing  wrong with the puzzle. I gave it my TU.

2.       Nothing  wrong with it being extracted from Wikipedia, OEIS or any math. textbook.

3.       Nothing  wrong with not sharing my opinion about its D-level. It was voiced prior to the publication. 

4.       I just claim that the effort needed to get it answered (i.e. the mental process through which one reaches two numbers i.e. 90 and 87360) is significantly less
than recently defined on the Forum as fitting D3.

5.       There is no analytical solution,   the existence of the 5th UP number is presently an unresolved math problem (both facts obscure to an innocent solver), therefore
one is driven either  to waste his time by trying in vain to "invent the wheel" or to write a program (with a limit set by someone who knows how futile is a longer trial), while  both  the 4 known numbers and a 2-line Mathematica statement to generate them exist on OEIS.
The above facts caused me to add a discouraging comment re the current "state of art".

6.       I am neither the first nor the only one to address the D-level issue.

Please read attentively "Two happy ends" (published in 2011), both the the puzzle  and the comments, that were triggered by 1st solver remark.

  The discussion that followed might be a good example of professional dialog, fully resolving flaws and misjudgments and  sharpening the solving tools of all involved.

<o:p> 7. Steve, the problem is not trivial. But one should not ignore the existence of OEIS and Internet, the best handbooks so easily  accessable.

Anyway, thanks for sharing with me your criteria.</o:p>

  Posted by Ady TZIDON on 2013-12-17 04:25:33
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