For an creature

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




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

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

." 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

Weisstein, Eric W. "Greatest prime Factor."From betterworld2016.org--A betterworld2016.org internet Resource. Https://betterworld2016.org/GreatestPrimeFactor.html

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