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Search: id:A067742
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| A067742 |
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Number of middle divisors of n, i.e. divisors in the half-open interval [sqrt(n/2), sqrt(n*2)). |
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+0
6
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| 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 0, 2, 1, 0, 1, 0, 2, 0, 0, 0, 2, 1, 0, 0, 2, 0, 2, 0, 1, 0, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 1, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 1, 2, 1, 0, 0, 0, 2, 0
(list; graph; listen)
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OFFSET
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1,6
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COMMENT
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a(A128605(n)) = n and a(m) <> n for m < A128605(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 14 2007
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REFERENCES
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Problem 10847, Amer. Math. Monthly 109, (2002), p. 80.
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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G.f.: sum((-1)^(k-1)*q^(k+1 choose 2)/(1-q^k), k, 1, inf)
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EXAMPLE
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a(6)=2 because 2 divisors of 6 (i.e. 2 and 3) are between sqrt(3) and sqrt(12).
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PROGRAM
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(PARI from M. F. Hasler, May 12 2008) A067743(n)=sumdiv( n, d, d*d<n/2 || d*d >= 2*n )
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CROSSREFS
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Cf. A067743, A071090.
A071562 lists all n such that a(n) is nonzero.
Sequence in context: A085861 A077266 A129561 this_sequence A089233 A066620 A025427
Adjacent sequences: A067739 A067740 A067741 this_sequence A067743 A067744 A067745
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KEYWORD
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easy,nonn
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Jan 29 2002
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