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.

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