Tau and Prime

A natural number n > 1 n>1 is called as special , if n = p p q q p + q n=p^{|p-q|}q^{p+q} with p p and q q different primes. Define h ( n ) h(n) for n > 1 n>1 natural as product of prime numbers that less than or equal to n n . If τ ( n ) \tau(n) is the number of positive divisors of n n , then find the smallest natural number a a such that τ ( a h ( τ ( a ) ) ) \large \tau(ah(\tau(a))) special .


The answer is 176.

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