Let $N$ = $2^1$$^5%$$3^1$$^6$. How many divisors of $N^2$ less than $N$ are there which don't divide $N$
MY ATTEMPT:
We have:
$N^2$ = $2^3$$^0%$$3^3$$^2$. The number of divisors of $N^2$ which do divide N should be of the form:
$2^a$$3^b$, where $a$ is a factor of 15 and $b$ a factor of 16
so, $a$ = 0, 3, 5, 15
$b$ = 0, 2, 4, 8, 16.
So, we have $5^4$ combinations.
The total number of divisors of $N^2$ are $1023$.
So, the total number which dont satisfy this condition:
$1023$ - $625$ = $398$, which is not the answer
The answer is somehow 240
Can someone help?