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.

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Other tasks:

Show that they cannot be semi-prime.

Show they must be square-free.