

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
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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]] (* JeanFrançois 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: A247180 A048839 A122144 * A248792 A064594 A240370
Adjacent sequences: A064049 A064050 A064051 * A064053 A064054 A064055


KEYWORD

nonn,easy


AUTHOR

Dean Hickerson, Aug 28 2001


STATUS

approved



