*
*

For an creature

*
=2" />, let
*
denote the greatest prime element of
*
, i.e., the number
*
in the factorization


*

with

*
*

A number for which

*
sqrt(n)" /> is called an unusual number through Greene and also Knuth (1990) and also a
*
-rough numbers by Finch (2001). The first couple of
*
-rough numbers are 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 20, 21, ... (OEIS A064052). The probability the a random optimistic integer is
*
-rough is
*
(Schroeppel 1972).

You are watching: How to find the greatest prime factor

A number that is not

*
-rough is called, not surprisingly, a
*
-smooth number (or sometimes, a "round number"). The first couple of are 1, 4, 8, 9, 12, 16, 18, 24, 25, 27, ... (OEIS A048098).


SEE ALSO: Dickman Function, distinct Prime Factors, Factor, Golomb-Dickman Constant, Least typical Multiple, the very least Prime Factor, Mangoldt Function, element Factor, prime Factorization, element Number, turbulent Number, Semiprime, Størmer Number, twin Peaks
REFERENCES:

Erdős, P. And Pomerance, C. "On the biggest Prime factors of

*
and
*
." Aequationes Math. 17, 211-321, 1978.

Finch, S. "RE: unusual Numbers." 27 Aug 2001. Http://listserv.nodak.edu/scripts/wa.exe?A2=ind0108&L=nmbrthry&P=963.

Greene, D.H. And Knuth, D.E. Mathematicsfor the analysis of Algorithms, third ed. Boston, MA: Birkhäuser, 1990.

Guy, R.K. "The biggest Prime variable of

*
." §B46 in Unsolved problems in Number Theory, 2nd ed. Brand-new York: Springer-Verlag, p.101, 1994.

Heath-Brown, D.R. "The largest Prime variable of the Integers in one Interval."Sci. China Ser. A 39, 449-476, 1996.

Mahler, K. "On the best Prime factor of

*
." Nieuw Arch. Wisk. 1, 113-122, 1953.

Schroeppel, R. Item 29 in Beeler, M.; Gosper, R.W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT artificial Intelligence Laboratory, Memo AIM-239, p.13, Feb. 1972. Http://www.inwap.com/pdp10/hbaker/hakmem/number.html#item29.

Sloane, N.J.A. Sequences A006530/M0428, A048098, and A064052 in "The On-Line Encyclopedia of essence Sequences."


Referenced top top betterworld2016.org|Alpha: greatest Prime Factor
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