Product representation of totient

Theorem

The following formula holds for distinct primes $p$ dividing $n$: $$\phi(n)=n \displaystyle\prod_{p | n} \left[ 1 - \dfrac{1}{p} \right],$$ where $\phi$ denotes the totient.

References

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $24.3.2 \mathrm{I}.C.$