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Search: id:A075989
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| A075989 |
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Number of k satisfying 1<=k<=n and <n/k> >= 1/2, where <n/k> is the fractional part of n/k; i.e. <n/k>=n/k-Floor(n,k). |
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+0
3
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| 0, 0, 1, 0, 2, 1, 2, 2, 3, 2, 5, 2, 4, 5, 6, 3, 6, 6, 7, 6, 7, 6, 11, 6, 8, 9, 10, 9, 12, 9, 10, 10, 13, 12, 15, 10, 11, 14, 17, 12, 16, 13, 16, 15, 16, 17, 20, 15, 16, 18, 19, 16, 23, 20, 21, 18, 19, 20, 25, 20, 22, 23, 26, 21, 24, 21, 24, 27, 28, 25, 28, 22, 25, 28, 29, 26, 31, 30
(list; graph; listen)
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OFFSET
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1,5
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FORMULA
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a(n)+A075988(n)=n-d(n), where d(n)=A000005(n) is the number of divisors of n.
a(n) seems to be asymptotic to c*n with c=0.61.... - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 03 2002
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EXAMPLE
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For n = 5, the fractional parts of k/n are 0, 1/2, 2/3, 1/4, 0; a(n) = 2 counts 1/2 and 2/3. A075988(5) = 1 counts 1/4, and A000005(5) = 2 counts the 0's.
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PROGRAM
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(PARI) a(n)=n-sum(i=1, n, if(sign(frac(n/i)-1/2)+1, 0, 1))
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CROSSREFS
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Cf. A075988, A076991.
Adjacent sequences: A075986 A075987 A075988 this_sequence A075990 A075991 A075992
Sequence in context: A127685 A127687 A024156 this_sequence A085432 A029169 A129193
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Sep 28 2002
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