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A099777 Number of divisors of 2n. 6
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; text; internal format)
OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

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

a(n) = A000005(n) + A001227(n). - Matthew Vandermast, Sep 30 2014

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

EXAMPLE

Example: a(7)=4 because the divisors of 14 are: 1,2,7 and 14.

MAPLE

with(numtheory): seq(tau(2*n), n=1..100);

MATHEMATICA

DivisorSigma[0, 2*Range[100]] (* Vladimir Joseph Stephan Orlovsky, Jul 20 2011 *)

PROG

(PARI) a(n)=if(n<1, 0, numdiv(2*n)) /* Michael Somos, Sep 20 2005 */

CROSSREFS

Bisection of A000005.

Cf. A000005, A099774.

Sequence in context: A029085 A087875 A195848 * A221917 A131798 A206925

Adjacent sequences:  A099774 A099775 A099776 * A099778 A099779 A099780

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 19 2004

EXTENSIONS

More terms from Emeric Deutsch, Dec 03 2004

STATUS

approved

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Last modified July 17 02:10 EDT 2019. Contains 325092 sequences. (Running on oeis4.)