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Sequence starting with 30 (Posted on 2016-07-05) Difficulty: 3 of 5
The prime factors of 30 are {2,3,5}
The sum of the reciprocals is 1/2+1/3+1/5=31/30
The product of the reciprocals is 1/2*1/3*1/5=1/30
The difference of the two is 31/30-1/30=1

There aren't many numbers where the final value of this procedure is a whole number.

Find more.

Other tasks:
Show that they cannot be semi-prime.
Show they must be square-free.

No Solution Yet Submitted by Jer    
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Some Thoughts Not semi-prime (proof) | Comment 2 of 3 |
If k is semi-prime, then k's prime factors are a and b, both > 1.

(1/a + 1/b) - 1/ab = (b+a-1)/ab

This equals 1 only if ab = b+a-1

Solving for a gives a = 1, which is a contradiction.

So k cannot be semi-prime 

  Posted by Steve Herman on 2016-07-05 18:13:38
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