Search: id:A048098
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%I A048098
%S A048098 1,4,8,9,12,16,18,24,25,27,30,32,36,40,45,48,49,50,54,56,60,63,64,70,
%T A048098 72,75,80,81,84,90,96,98,100,105,108,112,120,121,125,126,128,132,135,
%U A048098 140,144,147,150,154,160,162,165,168,169,175,176,180,182,189,192,195
%N A048098 Sqrt(n)-smooth numbers: if n = Product p_i^e_i then n >= (max p_i)^2.
%C A048098 This set (let 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 | Lpf(k) <=x } where Lpf(k) denotes the 
               largest 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
%H A048098 T. D. Noe, <a href="b048098.txt">Table of n, a(n) for n=1..1000</a>
%H A048098 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GreatestPrimeFactor.html">Greatest Prime Factor</a>
%H A048098 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RoundNumber.html">Round Number</a>
%o A048098 (PARI) for(n=1,1000,if(vecmax(component(factor(n),1))<=sqrt(n),print1(n,
               ",")))
%Y A048098 Cf. A063538, A063539, A063762, A063763, A064052.
%Y A048098 Sequence in context: A162966 A034043 A053443 this_sequence A122145 A057109 
               A069189
%Y A048098 Adjacent sequences: A048095 A048096 A048097 this_sequence A048099 A048100 
               A048101
%K A048098 easy,nonn,nice
%O A048098 1,2
%A A048098 J. Lowell (jhbubby(AT)avana.net)
%E A048098 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 22 2000

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