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A099777
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Number of divisors of 2n.
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1
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2, 3, 4, 4, 4, 6, 4, 5, 6, 6, 4, 8, 4, 6, 8, 6, 4, 9, 4, 8, 8, 6, 4, 10, 6, 6, 8, 8, 4, 12, 4, 7, 8, 6, 8, 12, 4, 6, 8, 10, 4, 12, 4, 8, 12, 6, 4, 12, 6, 9, 8, 8, 4, 12, 8, 10, 8, 6, 4, 16, 4, 6, 12, 8, 8, 12, 4, 8, 8, 12, 4, 15, 4, 6, 12, 8, 8, 12, 4, 12, 10, 6, 4, 16, 8, 6, 8, 10, 4, 18, 8, 8, 8, 6, 8
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Moebius transform is period 2 sequence [2, 1, ...]. - Michael Somos Sep 20 2005
G.f.: Sum_{k>0} x^k(2+x^k)/(1-x^(2k)) = Sum_{k>0} 2*x^(2k-1)/(1-x^(2k-1))+x^(2k)/(1-x^(2k)) . - Michael Somos Sep 20 2005
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EXAMPLE
| Example: a(7)=4 because the divisors of 14 are: 1,2,7 and 14.
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MAPLE
| with(numtheory): seq(tau(2*n), n=1..100);
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MATHEMATICA
| DivisorSigma[0, 2*Range[100]] (* From Vladimir Joseph Stephan Orlovsky, Jul 20 2011 *)
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PROG
| (PARI) a(n)=if(n<1, 0, numdiv(2*n)) /* Michael Somos Sep 20 2005 */
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CROSSREFS
| Bisection of A000005.
Cf. A000005, A099774.
Sequence in context: A029085 A087875 A195848 * A131798 A114212 A108355
Adjacent sequences: A099774 A099775 A099776 * A099778 A099779 A099780
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 19 2004
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 03 2004
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