|
| |
|
|
A048098
|
|
Sqrt(n)-smooth numbers: if p | n then p^2 <= n when p is prime.
|
|
10
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| This set (say S) has density d(S) = 1-Log(2) and multiplicative density m(S) = 1-exp(-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, (1-1/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 (Erdos and Davenport, 1951). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 12 2002
|
|
|
LINKS
| William A. Tedeschi, Table of n, a(n) for n=1..10000 [This replaces an earlier b-file computed by T. D. Noe]
Eric Weisstein's World of Mathematics, Greatest Prime Factor
Eric Weisstein's World of Mathematics, Round Number
|
|
|
FORMULA
| A006530(a(n)) ^ 2 <= a(n). [Reinhard Zumkeller, Oct 12 2011]
|
|
|
MATHEMATICA
| gpf[n_] := FactorInteger[n][[-1, 1]]; A048098 = {}; For[n = 1, n <= 200, n++, If[ gpf[n] <= Sqrt[n], AppendTo[ A048098, n] ] ]; A048098 (* From Jean-François Alcover, Jan 26 2012 *)
|
|
|
PROG
| (PARI) for(n=1, 1000, if(vecmax(factor(n)[, 1])<=sqrt(n), print1(n, ", ")))
(Haskell)
a048098 n = a048098_list !! (n-1)
a048098_list = [x | x <- [1..], a006530 x ^ 2 <= x]
-- Reinhard Zumkeller, Oct 12 2011
|
|
|
CROSSREFS
| Cf. A063538, A063539, A063762, A063763, A064052.
Sequence in context: A162966 A034043 A053443 * A122145 A057109 A069189
Adjacent sequences: A048095 A048096 A048097 * A048099 A048100 A048101
|
|
|
KEYWORD
| easy,nonn,nice
|
|
|
AUTHOR
| J. Lowell (jhbubby(AT)avana.net)
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 22 2000
Edited by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Nov 08 2010
|
| |
|
|
