Largest prime power 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. The largest prime power divisor of $n$, sometimes denoted $q(n)$ and sometimes denoted $a(n)$, is defined as the largest prime power that divides $n$.

Behavior

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A034699

Lower bound

Further information: Largest prime power divisor has logarithmic lower bound

The largest prime power divisor of $n$ is greater than $\log n$. Thus, we have:

$\underset{n\to \mathrm{\infty }}{lim}q(n)=\mathrm{\infty }$.

Asymptotic fraction

Further information: Fractional distribution of largest prime power divisor

The value of $\log (q(n))/\log n$ is almost uniformly distributed in the interval $[0,1]$.