Search: id:A002805
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%I A002805 M1589 N0619
%S A002805 1,2,6,12,60,20,140,280,2520,2520,27720,27720,360360,360360,360360,
%T A002805 720720,12252240,4084080,77597520,15519504,5173168,5173168,118982864,
%U A002805 356948592,8923714800,8923714800,80313433200,80313433200,2329089562800
%N A002805 Denominators of harmonic numbers H(n)=Sum 1/i.
%C A002805 H(n) is the maximal distance that a stack of n cards can project beyond 
               the edge of a table without toppling.
%C A002805 If n is not in {1,2,6} then a(n) has at least one prime factor other 
               then 2 or 5 . E.g. a(5)=60 has a prime factor 3 and a(7)=140 has 
               a prime factor 7. This implies that every H(n)=A001008(n)/A002805(n), 
               n not from {1,2,6}, has an infinite decimal representation. For a 
               proof see the J. Havil reference. - W. Lang, Jun 29 2007
%D A002805 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002805 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002805 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, 
               Reading, MA, 1990, p. 259.
%D A002805 D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, 
               MA, Vol. 1, p. 615.
%D A002805 J. Havil, Gamma, (in German), Springer, 2007, p. 35-6; Gamma: Exploring 
               Euler's Constant, Princeton Univ. Press, 2003.
%H A002805 T. D. Noe, <a href="b002805.txt">Table of n, a(n) for n=1..200</a>
%H A002805 R. M. Dickau, <a href="http://mathforum.org/advanced/robertd/harmonic.html">
               Harmonic numbers and the book stacking problem</a>
%H A002805 N. J. A. Sloane, <a href="a1008.gif">Illustration of initial terms</a>
%H A002805 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               BookStackingProblem.html">Link to a section of The World of Mathematics.</
               a>
%H A002805 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HarmonicNumber.html">Link to a section of The World of Mathematics.</
               a>
%e A002805 H(n) = [ 1, 3/2, 11/6, 25/12, 137/60, 49/20, 363/140, 761/280, 7129/2520,
               ... ] = A001008/A002805.
%p A002805 ZL:=n->sum(1/i, i=2..n): a:=n->floor(denom(ZL(n))): seq(a(n), n=1..29); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 28 2007
%t A002805 Denominator[ Drop[ FoldList[ #1 + 1/#2 &, 0, Range[ 30 ] ], 1 ] ] - Harvey 
               P. Dale Feb 09 2000
%t A002805 Table[Denominator[HarmonicNumber[n]], {n, 1, 40}] - Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Apr 20 2006
%Y A002805 Cf. A001008.
%Y A002805 Cf. A075135.
%Y A002805 Sequence in context: A083001 A119862 A111936 this_sequence A117481 A083268 
               A085911
%Y A002805 Adjacent sequences: A002802 A002803 A002804 this_sequence A002806 A002807 
               A002808
%K A002805 nonn,easy,frac,nice
%O A002805 1,2
%A A002805 N. J. A. Sloane (njas(AT)research.att.com).
%E A002805 More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 20 2006

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