Euler's Totient phi(n) and divisors count function d(n) relationship

Related with my former post, I found the following statement also very interesting:

When both the totient, phi(n), value (a) and the divisors count (b) function, d(n) or tau(n), of n are factors of n, if both are multiplied, they are exactly the value of n, so a*b=n.

There is only one isolated counterexample at n=30, and I did not test over n>1000000, so it could be possible that other counterexamples were greater than 1000000.

I also asked about this question at the Mathematics Stack Exchange (link here). It might be trivial, but I do not see a single specific pattern in the values of n to justify it. Any hints are welcomed! 

UPDATE: finally it was proved by a kind fellow at MSE !!! (link here).