

A048098


Numbers n that are sqrt(n)smooth: if p  n then p^2 <= n when p is prime.


15



1, 4, 8, 9, 12, 16, 18, 24, 25, 27, 30, 32, 36, 40, 45, 48, 49, 50, 54, 56, 60, 63, 64, 70, 72, 75, 80, 81, 84, 90, 96, 98, 100, 105, 108, 112, 120, 121, 125, 126, 128, 132, 135, 140, 144, 147, 150, 154, 160, 162, 165, 168, 169, 175, 176, 180, 182, 189, 192, 195
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OFFSET

1,2


COMMENTS

A006530(a(n))^2 <= a(n).  Reinhard Zumkeller, Oct 12 2011
This set (say S) has density d(S) = 1Log(2) and multiplicative density m(S) = 1exp(Gamma). Multiplicative density : let A be a set of numbers, A(x) = { k in A  gpf(k) <=x } where gpf(k) denotes the greatest prime factor of k and let m(x)(A) = prod(p<=x, (11/p))*sum(k in A(x), 1/k). If lim x >infinity m(x)(A) exists = m(A), this limit is called "multiplicative density" of A (Erdős and Davenport, 1951).  Benoit Cloitre, Jun 12 2002


LINKS

T. D. Noe and William A. Tedeschi, Table of n, a(n) for n=1..10000 (first 1000 terms computed by T. D. Noe)
H. Davenport and P. Erdős, On sequences of positive integers, J. Indian Math. Soc. 15 (1951), pp. 1924.
Eric Weisstein's World of Mathematics, Greatest Prime Factor
Eric Weisstein's World of Mathematics, Round Number


MATHEMATICA

gpf[n_] := FactorInteger[n][[1, 1]]; A048098 = {}; For[n = 1, n <= 200, n++, If[ gpf[n] <= Sqrt[n], AppendTo[ A048098, n] ] ]; A048098 (* JeanFrançois Alcover, Jan 26 2012 *)


PROG

(PARI) for(n=1, 1000, if(vecmax(factor(n)[, 1])<=sqrt(n), print1(n, ", ")))
(Haskell)
a048098 n = a048098_list !! (n1)
a048098_list = [x  x < [1..], a006530 x ^ 2 <= x]
 Reinhard Zumkeller, Oct 12 2011


CROSSREFS

Set union of A063539 and A001248.
Cf. A063538, A063762, A063763, A064052.
Sequence in context: A034043 A278517 A053443 * A322109 A122145 A328014
Adjacent sequences: A048095 A048096 A048097 * A048099 A048100 A048101


KEYWORD

easy,nonn,nice


AUTHOR

J. Lowell


EXTENSIONS

More terms from James A. Sellers, Apr 22 2000
Edited by Charles R Greathouse IV, Nov 08 2010


STATUS

approved



