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Search: id:A048098
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| A048098 |
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Sqrt(n)-smooth numbers: if n = Product p_i^e_i then n >= (max p_i)^2. |
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+0
9
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Greatest Prime Factor
Eric Weisstein's World of Mathematics, Round Number
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PROGRAM
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(PARI) for(n=1, 1000, if(vecmax(component(factor(n), 1))<=sqrt(n), print1(n, ", ")))
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CROSSREFS
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Cf. A063538, A063539, A063762, A063763, A064052.
Sequence in context: A162966 A034043 A053443 this_sequence A122145 A057109 A069189
Adjacent sequences: A048095 A048096 A048097 this_sequence A048099 A048100 A048101
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KEYWORD
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easy,nonn,nice
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AUTHOR
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J. Lowell (jhbubby(AT)avana.net)
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 22 2000
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