A064052 Not sqrt(n)-smooth: some prime factor of n is > sqrt(n).

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

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

Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

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][[-1, 1]]; If[f > Sqrt[n], Sow[n]]]][[2, 1]] (* Jean-François 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)) ) } \\ Harry J. Smith, Sep 06 2009

Crossrefs

Cf. A048098, A063538, A063539.

Sequence in context: A048839 A360477 A122144 * A248792 A358976 A064594

Adjacent sequences: A064049 A064050 A064051 * A064053 A064054 A064055

Keyword

nonn,easy

Author

Dean Hickerson, Aug 28 2001

Status

approved