least prime factor

The least prime factor of a positive integer $n$ is the smallest positive prime number dividing $n$. Sometimes expressed as a function, $\text{lpf}(n)$. For example, $\text{lpf}(91)=7$. For a prime number $p$, clearly $\text{lpf}(p)=p$, while for any composite number (except squares of primes) . (The function would be quite useless if 1 is considered a prime, therefore $\text{lpf}(1)$ is undefined — though we could make an argument for $\text{lpf}(0)=2$). In the sequence of least prime factors for each integer in turn, each prime occurs first at the index for itself then not again until its square.

In Mathematica, one can use LeastPrimeFactor[n] after loading a number theory package, or much more simply by using the command FactorInteger[n][[1,1]] (of course substituting n as necessary).

Title	least prime factor
Canonical name	LeastPrimeFactor
Date of creation	2013-03-22 17:40:03
Last modified on	2013-03-22 17:40:03
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	5
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A51