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Search: id:A102722
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| A102722 |
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Given n, sum all division remainders {n/k}, with k=1,...,n. The value a(n) is given by the floor of that sum. Note that {x}:=x-[x]. |
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+0
2
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| 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 4, 2, 4, 4, 4, 4, 6, 4, 7, 5, 6, 7, 9, 6, 8, 9, 10, 8, 11, 8, 11, 10, 11, 13, 14, 10, 13, 14, 15, 13, 16, 13, 17, 16, 15, 17, 20, 16, 18, 17, 19, 18, 22, 20, 21, 19, 20, 22, 26, 19, 23, 25, 24, 23, 25, 23, 26, 26, 28, 26, 30, 23, 27, 29, 29, 29, 31, 29, 33
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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Conjecture: a(n) ~ (1-EulerGamma)n
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FORMULA
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Contribution from Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Aug 25 2009: (Start)
a(n)=floor(n*H(n))-Sum_{1->n}(d(n)) ,where d(n) is the number of divisors of n, and H(n) is the nth Harmonic Number
a(n)=A052488(n)-A006218(n) (End)
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EXAMPLE
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a(5)= [{5/1}+{5/2}+{5/3}+{5/4}+{5/5}]=[0+0.5+0.6666+0.2+0]=[1.3666]=1 (division by 1 or by the number itself is to be avoided).
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MATHEMATICA
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Resto = Function[n, Sum[n/k - Floor[n/k], {k, 2, n - 1}]]; Floor[Map[Resto, Range[1, 1000]]]
Contribution from Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Aug 25 2009: (Start)
Table[Floor[n*HarmonicNumber[n]] - Sum[DivisorSigma[0, k], {k, 1, n}], {n, 1, 200}]
Table[Floor[Sum[FractionalPart[n/k], {k, 1, n}]], {n, 1, 200}] (End)
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CROSSREFS
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a(n)=A052488(n)-A006218(n) [From Barbarel Tres Mil (barbarel3000(AT)yahoo.es), Aug 25 2009]
Sequence in context: A161833 A139318 A054541 this_sequence A020475 A131183 A133770
Adjacent sequences: A102719 A102720 A102721 this_sequence A102723 A102724 A102725
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KEYWORD
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easy,nonn
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AUTHOR
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Carlos Alves (cjsalves(AT)gmail.com), Feb 06 2005
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