##  [Powerful Number](/powerful-number) 

  ##  [Powerful Number](https://puremath.quantumdictionary.io/powerful-number-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A positive integer n is called powerful if for every prime p dividing n, p^2 also divides n; equivalently, in the prime factorization n = ∏ p_i^{α_i}, every exponent α_i ≥ 2.