Search: id:A051037
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%I A051037
%S A051037 1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,27,30,32,36,40,45,48,50,54,60,
%T A051037 64,72,75,80,81,90,96,100,108,120,125,128,135,144,150,160,162,180,192,
%U A051037 200,216,225,240,243,250,256,270,288,300,320,324,360,375,384,400,405
%N A051037 5-smooth numbers: i.e. numbers whose prime divisors are all <= 5.
%C A051037 Sometimes called the Hamming sequence, since Hamming asked for an efficient 
               algorithm to generate the list, in ascending order, of all numbers 
               of the form 2^i3^j5^k for i,j,k >= 0. The problem was popularized 
               by Edsger Dijkstra.
%C A051037 Successive numbers k such that 8 k = EulerPhi[30 k]. [From Artur Jasinski 
               (grafix(AT)csl.pl), Nov 05 2008]
%C A051037 Where record values greater than 1 occur in A165704: A165705(n)=A165704(a(n)). 
               [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 26 
               2009]
%H A051037 T. D. Noe, <a href="b051037.txt">Table of n, a(n) for n=1..1000</a>
%H A051037 M. J. Dominus, <a href="http://perl.plover.com/Stream/stream.html">Infinite 
               Lists in Perl</a>.
%H A051037 Sci.math, <a href="http://groups.google.com/groups?dq=&hl=en&lr=&ie=UTF-8&th=55ea20a088f414b2">
               Ugly numbers</a>
%H A051037 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SmoothNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A051037 Wikipedia, <a href="http://en.wikipedia.org/wiki/Regular_number">Regular 
               number</a> [From Artur Jasinski (grafix(AT)csl.pl), Nov 06 2008]
%F A051037 Let s(n)=Card(k | a(k)<n) and f(n) = ln(n*sqrt(30))^3/(6*ln(2)*ln(3)*ln(5)). 
               Then s(n) = f(n) + O(lnln(n)). For example s(10000000)=768 is well 
               approximated by f(10000000)=769, 3... - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Dec 30 2001
%t A051037 aa = {}; Do[If[8 n - EulerPhi[30 n] == 0, AppendTo[aa, n]], {n, 1, 405}]; 
               aa [From Artur Jasinski (grafix(AT)csl.pl), Nov 05 2008]
%o A051037 (PARI) test(n)= {m=n; forprime(p=2,5, while(m%p==0,m=m/p)); return(m==1)} 
               for(n=1,500,if(test(n),print1(n",")))
%o A051037 (PARI) a(n)=local(m); if(n<1,0,n=a(n-1); until(if(m=n, forprime(p=2,5, 
               while(m%p==0,m/=p)); m==1),n++); n)
%Y A051037 For p-smooth numbers with other values of p, see A003586, A002473, A051038, 
               A080197, A080681, A080682, A080683.
%Y A051037 Cf. A112757, A112758, A112759, A112763, A112764, A003593.
%Y A051037 A159991, A159993, A159995. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 02 2009]
%Y A051037 Sequence in context: A097752 A014866 A051661 this_sequence A070023 A035303 
               A018609
%Y A051037 Adjacent sequences: A051034 A051035 A051036 this_sequence A051038 A051039 
               A051040
%K A051037 easy,nonn
%O A051037 1,2
%A A051037 Eric Weisstein (eric(AT)weisstein.com)

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