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A063539 Numbers n that are sqrt(n-1)-smooth: largest prime factor of n (=A006530(n)) < sqrt(n). 12


%S 1,8,12,16,18,24,27,30,32,36,40,45,48,50,54,56,60,63,64,70,72,75,80,

%T 81,84,90,96,98,100,105,108,112,120,125,126,128,132,135,140,144,147,

%U 150,154,160,162,165,168,175,176,180,182,189,192,195,196

%N Numbers n that are sqrt(n-1)-smooth: largest prime factor of n (=A006530(n)) < sqrt(n).

%C Sometimes (Weisstein) called the "usual numbers" as opposed to what Greene and Knuth define as "unusual numbers" (A063538), which turn out to not be so unusual after all (Greene and Knuth 1990, Finch 2001). - _Jonathan Vos Post_, Sep 11 2010

%D Greene, D. H. and Knuth, D. E., Mathematics for the Analysis of Algorithms, 3rd ed. Boston, MA: Birkhäuser, pp. 95-98, 1990.

%H Marius A. Burtea, <a href="/A063539/b063539.txt">Table of n, a(n) for n = 1..10622</a> (terms 1..1000 from T. D. Noe)

%H M. Beeler, R. W. Gosper and R. Schroeppel, <a href="http://www.inwap.com/pdp10/hbaker/hakmem/number.html#item29">HAKMEM, ITEM 29</a>

%H Steven Finch, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;1bd7a1c2.0108">"RE: Unusual Numbers."</a> Aug 27, 2001

%H Project Euler, <a href="https://projecteuler.net/problem=668">Problem 668: Square root smooth numbers</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/RoughNumber.html"> Rough Number.</a> [From _Jonathan Vos Post_, Sep 11 2010]

%p N:= 1000: # to get all terms <= N

%p Primes:= select(isprime, [2, seq(2*i+1, i=1..floor((N-1)/2))]):

%p S:= {$1..N} minus {seq(seq(m*p, m = 1 .. min(p, N/p)), p=Primes)}:

%p sort(convert(S, list)); # _Robert Israel_, Sep 02 2015

%t Prepend[Select[Range[192], FactorInteger[#][[-1, 1]] < Sqrt[#] &], 1] (* _Ivan Neretin_, Sep 02 2015 *)

%o (MAGMA) [1] cat [m:m in [2..200]| Max(PrimeFactors(m)) lt Sqrt(m) ]; // _Marius A. Burtea_, May 08 2019

%Y Set difference of A048098 and A001248.

%Y Complement of A063538.

%Y Cf. A006530.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Aug 14 2001

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)