

A063539


Numbers n that are sqrt(n1)smooth: largest prime factor of n (=A006530(n)) < sqrt(n).


12



1, 8, 12, 16, 18, 24, 27, 30, 32, 36, 40, 45, 48, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 98, 100, 105, 108, 112, 120, 125, 126, 128, 132, 135, 140, 144, 147, 150, 154, 160, 162, 165, 168, 175, 176, 180, 182, 189, 192, 195, 196
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OFFSET

1,2


COMMENTS

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


REFERENCES

Greene, D. H. and Knuth, D. E., Mathematics for the Analysis of Algorithms, 3rd ed. Boston, MA: BirkhĂ¤user, pp. 9598, 1990.


LINKS

Marius A. Burtea, Table of n, a(n) for n = 1..10622 (terms 1..1000 from T. D. Noe)
M. Beeler, R. W. Gosper and R. Schroeppel, HAKMEM, ITEM 29
Steven Finch, "RE: Unusual Numbers." Aug 27, 2001
Project Euler, Problem 668: Square root smooth numbers
Eric W. Weisstein, Rough Number. [From Jonathan Vos Post, Sep 11 2010]


MAPLE

N:= 1000: # to get all terms <= N
Primes:= select(isprime, [2, seq(2*i+1, i=1..floor((N1)/2))]):
S:= {$1..N} minus {seq(seq(m*p, m = 1 .. min(p, N/p)), p=Primes)}:
sort(convert(S, list)); # Robert Israel, Sep 02 2015


MATHEMATICA

Prepend[Select[Range[192], FactorInteger[#][[1, 1]] < Sqrt[#] &], 1] (* Ivan Neretin, Sep 02 2015 *)


PROG

(MAGMA) [1] cat [m:m in [2..200] Max(PrimeFactors(m)) lt Sqrt(m) ]; // Marius A. Burtea, May 08 2019


CROSSREFS

Set difference of A048098 and A001248.
Complement of A063538.
Cf. A006530.
Sequence in context: A192991 A083348 A174261 * A253296 A081925 A049199
Adjacent sequences: A063536 A063537 A063538 * A063540 A063541 A063542


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Aug 14 2001


STATUS

approved



