Search: id:A013936
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%I A013936
%S A013936 1,2,3,5,6,7,8,10,12,13,14,16,17,18,19,22,23,25,26,28,29,30,31,33,35,
%T A013936 36,38,40,41,42,43,46,47,48,49,53,54,55,56,58,59,60,61,63,65,66,67,70,
%U A013936 72,74,75,77,78,80,81,83,84,85,86,88,89,90,92,96,97,98,99,101,102,103
%N A013936 Sum_{k=1..n} floor(n/k^2).
%D A013936 T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 
               1976, page 73, problem 24.
%H A013936 Franklin T. Adams-Watters, <a href="b013936.txt">Table of n, a(n) for 
               n = 1..10000</a>
%F A013936 a(n)=a(n-1)+A046951(n). Bounded above by n*pi^2/6: the growth of the 
               differences seems to be roughly proportional to sqrt(n). - Henry 
               Bottomley (se16(AT)btinternet.com), Aug 16 2001
%F A013936 Conjecture : limit n ->infinity (pi^2/6*n-a(n))/sqrt(n) = c = 1.45... 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 10 2003
%F A013936 If lim_{n->infinity} (Pi^2/6*n - a(n)) / sqrt(n) does exist, it converges 
               very slowly. It does appear to be bounded. - Franklin T. Adams-Watters 
               (FrankTAW(AT)Netscape.net), Nov 17 2006
%p A013936 f := n->sum(floor(n/k^2),k=1..n); [ seq(f(j),j=1..100 ];
%Y A013936 Sequence in context: A028765 A059870 A145353 this_sequence A076437 A028790 
               A028748
%Y A013936 Adjacent sequences: A013933 A013934 A013935 this_sequence A013937 A013938 
               A013939
%K A013936 nonn
%O A013936 1,2
%A A013936 N. J. A. Sloane (njas(AT)research.att.com), Henri Lifchitz (100637.64(AT)CompuServe.COM)

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