just one. 3^6=729.
The number of divisors can be computed by looking at the prime factorization
(p1^a1)(p2^a2)...
and is given by the product
(a1+1)(a2+1)...
Since 7 is prime, the only product is
(a1+1)=7
a1 = 6
So only number if the form p^6 have 7 divisors.
And only 3^6 is a 3 digit number.

Posted by Jer
on 20150313 08:50:08 