1.

Let `n=180`. Find the number of positive integral divisors of `n^2`, which do not divide n

Answer» n=180=20*4
n=`2^2*3^2*5`
`D_1=(2+1)(2+1)(1+1)-1`
`D_1=17-(1)`
`n^2=2^4*3^4*5^2`
`D_2=(4+1)(4+1)(3)-2`
`D_2=73-(2)`
subtracting equation 1 from 2
=73-17=56 is our required number.


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