Search: id:A102722
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%I A102722
%S A102722 0,0,0,0,1,0,2,1,2,2,4,2,4,4,4,4,6,4,7,5,6,7,9,6,8,9,10,8,11,8,11,10,11,
%T A102722 13,14,10,13,14,15,13,16,13,17,16,15,17,20,16,18,17,19,18,22,20,21,19,
%U A102722 20,22,26,19,23,25,24,23,25,23,26,26,28,26,30,23,27,29,29,29,31,29,33
%N A102722 Given n, sum all division remainders {n/k}, with k=1,...,n. The value 
               a(n) is given by the floor of that sum. Note that {x}:=x-[x].
%C A102722 Conjecture: a(n) ~ (1-EulerGamma)n
%F A102722 Contribution from Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Aug 25 
               2009: (Start)
%F A102722 a(n)=floor(n*H(n))-Sum_{1->n}(d(n)) ,where d(n) is the number of divisors 
               of n, and H(n) is the nth Harmonic Number
%F A102722 a(n)=A052488(n)-A006218(n) (End)
%e A102722 a(5)= [{5/1}+{5/2}+{5/3}+{5/4}+{5/5}]=[0+0.5+0.6666+0.2+0]=[1.3666]=1 
               (division by 1 or by the number itself is to be avoided).
%t A102722 Resto = Function[n, Sum[n/k - Floor[n/k], {k, 2, n - 1}]]; Floor[Map[Resto, 
               Range[1, 1000]]]
%t A102722 Contribution from Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Aug 25 
               2009: (Start)
%t A102722 Table[Floor[n*HarmonicNumber[n]] - Sum[DivisorSigma[0, k], {k, 1, n}], 
               {n, 1, 200}]
%t A102722 Table[Floor[Sum[FractionalPart[n/k], {k, 1, n}]], {n, 1, 200}] (End)
%Y A102722 a(n)=A052488(n)-A006218(n) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), 
               Aug 25 2009]
%Y A102722 Sequence in context: A161833 A139318 A054541 this_sequence A020475 A131183 
               A133770
%Y A102722 Adjacent sequences: A102719 A102720 A102721 this_sequence A102723 A102724 
               A102725
%K A102722 easy,nonn
%O A102722 0,7
%A A102722 Carlos Alves (cjsalves(AT)gmail.com), Feb 06 2005

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