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A006590
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Sum_{k=1..n} ceiling(n/k).
(Formerly M2522)
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12
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1, 3, 6, 9, 13, 16, 21, 24, 29, 33, 38, 41, 48, 51, 56, 61, 67, 70, 77, 80, 87, 92, 97, 100, 109, 113, 118, 123, 130, 133, 142, 145, 152, 157, 162, 167, 177, 180, 185, 190, 199, 202, 211, 214, 221, 228, 233, 236, 247, 251, 258, 263, 270, 273, 282, 287, 296, 301
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The following sequences all have the same parity: A004737, A006590, A027052, A071028, A071797, A078358, A078446. - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Mar 16 2003
Given the fact that ceiling(x) <= x+1, we can, using well known results for the harmonic series, easily derive that n*ln(n) <= a(n) <= n*(1+ln(n)) + n = n(ln(n)+2). - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006
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REFERENCES
| Marc LeBrun (mlb(AT)well.com), personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| a(n) = n+Sum_{k=1..n-1} tau(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 17 2002
a(n)=1+a(n-1)+tau(n-1), a(n)=A006218(n-1)+n - T. D. Noe, Jan 05 2007
a(n) = a(n-1) + A000005(n) + 1 for n >= 2. a(n) = A161886(n) - A000005(n) + 1 = A161886(n-1) + 2 = A006218(n) + A049820(n) for n >= 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Nov 14 2009]
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MATHEMATICA
| Table[Sum[Ceiling[n/i], {i, 1, n}], {n, 1, 60}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006
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CROSSREFS
| Cf. A000005, A006218.
Sequence in context: A066343 A184909 A060605 * A061781 A123753 A124288
Adjacent sequences: A006587 A006588 A006589 * A006591 A006592 A006593
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 08 2006
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