Thanks guest,

I did understand that.

Those numbers are how many factors any kinda-prime number less than 1000 can have.

I have no idea where to go from there.

You have collected some of them but I suspect there are many more. Umm...

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All factors are in pairs so all prime numbers have 2 factors, 2 is a prime number, so all prime numbers are sorta-prime as well.

There are 168 of those (could have worked it our using Sieve of Eratosthenes but I let someone else on the net do that for me)

Certainly at least some of the squared numbers work.

How about 10^2 ? 1 2 4 5 10 20 25 50 100 That has 9 factors so that is no good.

Squares of primes would all work becasue they have 3 factors: that is these ones squared 2,3,5,7,9,11,13,17,19,23,29,31, (that is 12)

Cubes of primes have 4 factors so they are no good.

primes to the power of 4 have 5 factors so they are all good. 2,3,4,5 (that is 3)

Primes to the power of 6 have 7 factors so they are all good 2 and 3 (that is 2)

So now I have 168 + 12+3+2 = 168+ 17

that is the same as what you got guest.

I can't think of any others either.

**You did well guest **