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Search: id:A066660
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| A066660 |
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Number of divisors of 2n excluding 1. |
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+0
4
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| 1, 2, 3, 3, 3, 5, 3, 4, 5, 5, 3, 7, 3, 5, 7, 5, 3, 8, 3, 7, 7, 5, 3, 9, 5, 5, 7, 7, 3, 11, 3, 6, 7, 5, 7, 11, 3, 5, 7, 9, 3, 11, 3, 7, 11, 5, 3, 11, 5, 8, 7, 7, 3, 11, 7, 9, 7, 5, 3, 15, 3, 5, 11, 7, 7, 11, 3, 7, 7, 11, 3, 14, 3, 5, 11, 7, 7, 11, 3, 11, 9, 5, 3, 15, 7, 5, 7, 9, 3, 17, 7, 7, 7, 5, 7
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) is the number of integers of the form (n+k)/(n-k) for k=0,1,2,...,n-1.
Inverse Moebius transform of A040001 (offset 1).
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FORMULA
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If n is prime a(n)=3. Asymptotic formula: 1/n*sum(i=1, n, a(i))=C*ln(n)+o(ln(n)) with C= .4... Also lim n -> infinity card(i<n, a(i) even)/card(i<n, a(i) odd) = 0.
G.f.: Sum_{n>0} x^n(1-x^(3n))/((1-x^n)(1-x^(2n))).
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EXAMPLE
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a(4)=3 because (4+0)/(4-0), (4+2)/(4-2), (4+3)/(4-3) are integers.
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PROGRAM
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(PARI) a(n)=if(n<1, 0, sumdiv(n, d, (d>1)+d%2))
(PARI) {a(n)=if(n<1, 0, numdiv(2*n)-1)} /* Michael Somos Sep 03 2006 */
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CROSSREFS
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Cf. A040001.
A069930(n) + 1.
Adjacent sequences: A066657 A066658 A066659 this_sequence A066661 A066662 A066663
Sequence in context: A064338 A103359 A020481 this_sequence A057957 A076559 A102601
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 11 2002
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