number theorem

For a positive integer n greater than 1 the prime factors can be decomposed:

n = p ₁ ^ a ₁ * p ₂ ^ a ₂ * p ₃ ^ a ₃ *… * p _k ^ a _k ,

Then the number of positive divisors of n is (a ₁ +1)(a ₂ +1)(a ₃ +1)…( _ak +1) .

where p ₁ , p ₂ , p _3, ...p _k are all prime factors of n;

a ₁ , a ₂ , a ₃ . . . ak are exponents of p ₁ , p ₂ , p _{3 ,} . . . p _{k .}