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A066660
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Number of divisors of 2n excluding 1.
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| 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
| a(4)=3 because (4+0)/(4-0), (4+2)/(4-2), (4+3)/(4-3) are integers.
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PROG
| (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 */
(PARI) { for (n=1, 1000, write("b066660.txt", n, " ", numdiv(2*n) - 1) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Mar 16 2010]
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CROSSREFS
| Cf. A040001.
A069930(n) + 1.
Sequence in context: A197592 A103359 A020481 * A057957 A076559 A102601
Adjacent sequences: A066657 A066658 A066659 * A066661 A066662 A066663
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 11 2002
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