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A063539 Numbers n that are sqrt(n-1)-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 (list; graph; refs; listen; history; text; internal format)
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: Birkhäuser, pp. 95-98, 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((N-1)/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

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Last modified January 20 19:53 EST 2020. Contains 331096 sequences. (Running on oeis4.)