Search: id:A057641
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%I A057641
%S A057641 0,0,1,0,4,0,7,2,7,5,13,0,17,9,12,8,23,5,27,8,21,20,34,1,33,25,
%T A057641 30,17,46,7,50,22,40,37,46,6,62,43,50,19,70,19,74,37,46,55,82,9,
%U A057641 79,46,70,47,95,32,83,38,81,74,107,2,112,81,76,56,102,45,125,70
%N A057641 Floor(H(n)+exp(H(n))*log(H(n))) - sigma(n), where H(n) = Sum_{k=1..n} 
               1/k and sigma(n) (A000203) is the sum of the divisors of n.
%C A057641 Showing this is nonnegative is equivalent to proving the Riemann hypothesis.
%D A057641 G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothese 
               de Riemann, J. Math. Pures Appl. 63 (1984), 187-213.
%H A057641 T. D. Noe, <a href="b057641.txt">Table of n, a(n) for n=1..10000</a>
%H A057641 J. C. Lagarias, <a href="http://arXiv.org/abs/math.NT/0008177">An elementary 
               problem equivalent to the Riemann hypothesis</a>, Am. Math. Monthly 
               109 (#6, 2002), 534-543.
%Y A057641 Cf. A057640, A000203, A076633, A067698.
%Y A057641 Sequence in context: A052400 A022895 A157698 this_sequence A133930 A077892 
               A117543
%Y A057641 Adjacent sequences: A057638 A057639 A057640 this_sequence A057642 A057643 
               A057644
%K A057641 nonn,nice,easy
%O A057641 1,5
%A A057641 N. J. A. Sloane (njas(AT)research.att.com), Oct 12 2000

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