Let n be a positive integer with exactly 3 positive prime divisors. If n^2 has 27 divisors, how many does n have?
n==30
30==2 * 3 * 5==3 prime factors
30==(1, 2, 3, 5, 6, 10, 15, 30)>>Total = 8 divisors
30^2= (1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900) > 27 (divisors)
+118667 Thanks Guest, you have utilized C++ (I assume) and answered for a specific case but this was reasonable.
I have given a more general answer. But I liked your answer 
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Let n be a positive integer with exactly 3 positive prime divisors. If n^2 has 27 divisors, how many does n have?
** All the pronumeral I have used are positive integers. a,b and c are also prime numbers
\(n=a^pb^qc^r\qquad \text{This will have }(p+1)(q+1)(r+1)\;\;factors\\ n^2=a^{2p}b^{2q}c^{2r} \qquad\text{This will have }(2p+1)(2q+1)(2r+1)\;\;factors \)
We are told that
\((2p+1)(2q+1)(2r+1)=27\)
Since p,q and r are all positive integer the smallest value that any of those brackets can take is 3
3^3=27
so that means that p=q=r=1
so n must have 2*2*2=8 factors.
LaTex:
n=a^pb^qc^r\qquad \text{This will have }(p+1)(q+1)(r+1)\;\;factors\\
n^2=a^{2p}b^{2q}c^{2r} \qquad\text{This will have }(2p+1)(2q+1)(2r+1)\;\;factors
