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
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
From Bernard Schott, Sep 14 2020: (Start)
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)
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 19 2004
EXTENSIONS
More terms from Emeric Deutsch, Dec 03 2004
STATUS
approved