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Search: id:A153818
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| A153818 |
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a(n)=Sum_{k=1..n} floor(n^2/k^2) |
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+0
3
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| 1, 5, 12, 22, 35, 53, 72, 96, 123, 153, 184, 222, 260, 304, 351, 402, 453, 510, 568, 633, 697, 765, 839, 916, 994, 1077, 1164, 1252, 1342, 1443, 1535, 1641, 1747, 1856, 1969, 2083, 2200, 2321, 2447, 2579, 2705, 2844, 2979, 3123, 3269, 3417, 3570, 3726, 3881
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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How to express Sum_{k=1..n} floor(n^2/k^2) as a function of Sum_{k=1..n} floor(n/k) ? [From Ctibor O. Zizka (c.zizka(AT)email.cz), Feb 14 2009]
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EXAMPLE
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a(4)=22 because floor(16/1)+floor(16/4)+floor(16/9)+floor(16,16)=16+4+1+1=22. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 13 2009]
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MAPLE
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a := proc (n) options operator, arrow: sum(floor(n^2/k^2), k = 1 .. n) end proc: seq(a(n), n = 1 .. 50); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 13 2009]
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CROSSREFS
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Cf. A006218
Sequence in context: A000326 A022795 A025734 this_sequence A069627 A034971 A025740
Adjacent sequences: A153815 A153816 A153817 this_sequence A153819 A153820 A153821
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KEYWORD
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easy,nonn
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AUTHOR
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Ctibor O. Zizka (c.zizka(AT)email.cz), Jan 02 2009
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EXTENSIONS
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Definition edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 13 2009
Extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 13 2009
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