Largest prime divisor

This article defines an arithmetic function or number-theoretic function: a function from the natural numbers to a ring (usually, the ring of integers, rational numbers, real numbers, or complex numbers).
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Definition

Let $n$ be a natural number greater than $1$. The largest prime divisor' of $n$ is defined as the largest among the primes $p$ that divide $n$. This is denoted as $a(n)$. By fiat, we set $a(1)=1$.

Behavior

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A006530

Lower bound

There is no lower bound on the largest prime divisor of $n$ as a function of $n$. There are infinitely many powers of two, and hence, $a(n)=2$ for infinitely many numbers.

Relation with other arithmetic functions

• Largest prime power divisor
• Largest square-free divisor