Problems & Puzzles: Puzzles

Puzzle 625. Sum of squares of prime divisors

After the generous acceptance of my friend Frank Rubin, I bring -from one of his always interesting pages, Contest Center- the following nice and unsolved puzzle:

Which whole numbers are equal to the sum of the squares of their prime divisors?

For example:
16=2󫎾2=2+2+2+2 and
27=3󫢫=3+3+3.

Q. Are there more cases, or these two are the unique examples?


Contributions came from J. K. Andersen

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Andersen wrote:

There are no other cases below 10^11.

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