Greatest Prime Factor

For an Integer $n\geq 2$, let $\mathop{\rm gpf}\nolimits (x)$ denote the greatest prime factor of $n$, i.e., the number $p_k$ in the factorization

$$n={p_1}^{a_1}\cdots{p_k}^{a_k},$$

with $p_i<p_j$ for $i<j$. For $n=2$, 3, ..., the first few are 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 3, 13, 7, 5, ... (Sloane's A006530). The greatest multiple prime factors for Squareful integers are 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 3, ... (Sloane's A046028).

See also Distinct Prime Factors, Factor, Least Common Multiple, Least Prime Factor, Mangoldt Function, Prime Factors, Twin Peaks

References

Erdös, P. and Pomerance, C. ``On the Largest Prime Factors of $n$ and $n+1$.'' Aequationes Math. 17, 211-321, 1978.

Guy, R. K. ``The Largest Prime Factor of $n$.'' §B46 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 101, 1994.

Heath-Brown, D. R. ``The Largest Prime Factor of the Integers in an Interval.'' Sci. China Ser. A 39, 449-476, 1996.

Mahler, K. ``On the Greatest Prime Factor of $ax^m+by^n$.'' Nieuw Arch. Wiskunde 1, 113-122, 1953.

Sloane, N. J. A. Sequence A006530/M0428 in ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.