Search: id:A002473
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%I A002473 M0477 N0177
%S A002473 1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,25,27,28,30,32,35,36,40,
%T A002473 42,45,48,49,50,54,56,60,63,64,70,72,75,80,81,84,90,96,98,100,105,108,
%U A002473 112,120,125,126,128,135,140,144,147,150,160,162,168,175,180,189,192
%N A002473 Highly composite numbers (2): numbers whose prime divisors are all <= 
               7.
%C A002473 Also called 7-smooth numbers or humble numbers.
%C A002473 Successive numbers k such EulerPhi[210 k] = 48 k. [From Artur Jasinski 
               (grafix(AT)csl.pl), Nov 05 2008]
%C A002473 The divisors of 10! (cf. A161466) are a finite subsequence. [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 10 2009]
%D A002473 B. C. Berndt, Ramanujan's Notebooks Part IV, Springer-Verlag, see p. 
               52.
%D A002473 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002473 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002473 N. J. A. Sloane, <a href="b002473.txt">Table of n, a(n) for n=1..5841</
               a> [All terms <2*10^9.]
%H A002473 University of Ulm, <a href="http://www.informatik.uni-ulm.de/acm/Locals/
               1996/number.sol">The first 5842 terms</a>
%H A002473 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SmoothNumber.html">Link to a section of The World of Mathematics.</
               a>
%t A002473 Select[Range[250], Max[Transpose[FactorInteger[ # ]][[1]]]<=7&]
%t A002473 aa = {}; Do[If[EulerPhi[210 n] == 48 n, AppendTo[aa, n]], {n, 1, 1200}]; 
               aa [From Artur Jasinski (grafix(AT)csl.pl), Nov 05 2008]
%o A002473 (PARI) test(n)= {m=n; forprime(p=2,7, while(m%p==0,m=m/p)); return(m==1)} 
               for(n=1,200,if(test(n),print1(n",")))
%Y A002473 Cf. A002182, A067374. Complement of A068191. Not the same as A063938. 
               For p-smooth numbers with other values of p, see A003586, A051037, 
               A051038, A080197, A080681, A080682, A080683.
%Y A002473 Sequence in context: A056757 A079333 A063938 this_sequence A161466 A117296 
               A096503
%Y A002473 Adjacent sequences: A002470 A002471 A002472 this_sequence A002474 A002475 
               A002476
%K A002473 nonn,easy,nice
%O A002473 1,2
%A A002473 N. J. A. Sloane (njas(AT)research.att.com).
%E A002473 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
%E A002473 Additional comments from Michel Lecomte, Jun 09 2007

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