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A064052 Not sqrt(n)-smooth: some prime factor of n is > sqrt(n). 10
2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 26, 28, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 46, 47, 51, 52, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 68, 69, 71, 73, 74, 76, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 97, 99, 101, 102 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This set (S say) has density d(S) = Log(2) - Benoit Cloitre, Jun 12 2002

Finch defines a positive integer N to be "jagged" if its largest prime factor is > sqrt(N). - Frank Ellermann, Apr 21 2011

REFERENCES

S. R. Finch, Mathematical Constants, 2003, chapter 2.21.

LINKS

Harry J. Smith, Table of n, a(n) for n=1,...,1000

Eric Weisstein's World of Mathematics, Greatest Prime Factor

EXAMPLE

9=3*3 is not "jagged", but 10=5*2 is "jagged": 5 > sqrt(10).

20=5*2*2 is "jagged", but not squarefree, cf. A005117.

MATHEMATICA

Reap[For[n = 2, n <= 102, n++, f = FactorInteger[n][[All, 1]]; s = Sqrt[n]; If[Count[f, p_ /; p > s] > 0, Sow[n]]]][[2, 1]] (* Jean-Fran├žois Alcover, May 16 2014 *)

PROG

(PARI) { n=0; for (m=2, 10^9, f=factor(m)~; if (f[1, length(f)]^2 > m, write("b064052.txt", n++, " ", m); if (n==1000, break)) ) } [From Harry J. Smith, Sep 06 2009]

CROSSREFS

Cf. A048098, A063538, A063539.

Sequence in context: A203076 A048839 A122144 * A064594 A240370 A193304

Adjacent sequences:  A064049 A064050 A064051 * A064053 A064054 A064055

KEYWORD

nonn,easy

AUTHOR

Dean Hickerson, Aug 28 2001

STATUS

approved

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Last modified September 2 08:30 EDT 2014. Contains 246339 sequences.