Re: smallest positive integer that has exactly k divisors

In article <1193203237.965221.68120@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mukesh tiwari <mukeshtiwari.iiitm@xxxxxxxxx> wrote:

Hello everybody . i have to find the smallest positive integer that
has exactly k divisors. for example if k=6 then 12 is the minimum
number which have 6 divisors.One brute force approach i came across
is find the prime factorization and calculate the divisors until
divisors are equal to the k but this one is taking to much time even
for 2000 factors .

Do you know the formula for the number of divisors of n,
given the prime factorization of n?
Can you set that formula equal to k and thus find which kinds
of prime factorization will lead to a number with exactly k divisors?

For example, do you know that for a number to have exactly 7 divisors,
the number must be the 6th power of a prime?

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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