The divisor function d(n) is defined as 'the number of positive divisors of n (including 1 and n)' according to Underwood Dudley.
Is the divisor function $d(n^2)$ related to $d(n)$?
d(10)=4 and $d(10^2)$=9
or d(14)=4 and $d(14^2)=9$
So can one find the $d(n^2)$ from knowing only d(n) and n through some relation or function?
Has any work been done on this problem?