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Search: id:A013936
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| A013936 |
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Sum_{k=1..n} floor(n/k^2). |
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+0
6
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| 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, 36, 38, 40, 41, 42, 43, 46, 47, 48, 49, 53, 54, 55, 56, 58, 59, 60, 61, 63, 65, 66, 67, 70, 72, 74, 75, 77, 78, 80, 81, 83, 84, 85, 86, 88, 89, 90, 92, 96, 97, 98, 99, 101, 102, 103
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 73, problem 24.
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LINKS
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Franklin T. Adams-Watters, Table of n, a(n) for n = 1..10000
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FORMULA
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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
Conjecture : limit n ->infinity (pi^2/6*n-a(n))/sqrt(n) = c = 1.45... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 10 2003
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
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MAPLE
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f := n->sum(floor(n/k^2), k=1..n); [ seq(f(j), j=1..100 ];
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CROSSREFS
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Sequence in context: A137620 A028765 A059870 this_sequence A076437 A028790 A028748
Adjacent sequences: A013933 A013934 A013935 this_sequence A013937 A013938 A013939
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KEYWORD
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nonn
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AUTHOR
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njas, Henri Lifchitz (100637.64(AT)CompuServe.COM)
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