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A099777
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Number of divisors of 2n.
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29
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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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
Sum_{k=1..n} a(k) ~ n/2 * (3*log(n) + log(2) + 6*gamma - 3), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Feb 13 2019
a(n) = 2 iff n = 1;
a(n) = prime(m) iff n = 2^(prime(m)-2);
a(n) = 4 iff n = 4 or n is an odd prime (A065091);
a(n) = 6 iff n = 16, or n = 2p for p an odd prime (A100484 \ {4}), or n = p^2 for p an odd prime (A001248 \ {4});
a(n) = 2*A000005(n) iff n is odd. (End)
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EXAMPLE
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a(7)=4 because the divisors of 14 are: 1,2,7 and 14.
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MAPLE
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with(numtheory): seq(tau(2*n), n=1..100);
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MATHEMATICA
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PROG
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(PARI) a(n)=if(n<1, 0, numdiv(2*n)) /* Michael Somos, Sep 20 2005 */
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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