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 A099774 Number of divisors of 2*n-1. 35
 1, 2, 2, 2, 3, 2, 2, 4, 2, 2, 4, 2, 3, 4, 2, 2, 4, 4, 2, 4, 2, 2, 6, 2, 3, 4, 2, 4, 4, 2, 2, 6, 4, 2, 4, 2, 2, 6, 4, 2, 5, 2, 4, 4, 2, 4, 4, 4, 2, 6, 2, 2, 8, 2, 2, 4, 2, 4, 6, 4, 3, 4, 4, 2, 4, 2, 4, 8, 2, 2, 4, 4, 4, 6, 2, 2, 6, 4, 2, 4, 4, 2, 8, 2, 3, 6, 2, 6, 4, 2, 2, 4, 4, 4, 8, 2, 2, 8, 2, 2, 4, 4, 4, 6, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 FORMULA G.f.: Sum_{k>0} x^k/(1-x^(2*k-1)). - Michael Somos, Sep 02 2006 G.f.: sum(k>=1, x^((2*k-1)^2/2+1/2) * (1+x^(2*k-1))/(1-x^(2*k-1)) ). - Joerg Arndt, Nov 08 2010 Dirichlet g.f. (with interpolated zeros): zeta(s)^2*(1-1/2^s)^2. - Geoffrey Critzer, Feb 15 2015 Sum_{k=1..n} a(k) ~ (n*log(n) + (2*gamma - 1 + 3*log(2))*n)/2, where gamma is Euler's constant (A001620). - Amiram Eldar, Nov 27 2022 EXAMPLE a(5)=3 because the divisors of 9 are: 1, 3 and 9. MAPLE with(numtheory): seq(tau(2*n-1), n=1..120); MATHEMATICA nn = 200; f[list_, i_] := list[[i]]; a =Table[Boole[OddQ[n]], {n, 1, nn}]; Select[Table[DirichletConvolve[f[a, n], f[a, n], n, m], {m, 1, nn}], # > 0 &] (* Geoffrey Critzer, Feb 15 2015 *) Table[DivisorSigma[0, 2*n-1], {n, 1, 100}] (* Vaclav Kotesovec, Jan 14 2019 *) PROG (PARI) {a(n)=if(n<1, 0, numdiv(2*n-1))} /* Michael Somos, Sep 03 2006 */ (Haskell) a099774 = a000005 . a005408 -- Reinhard Zumkeller, Sep 22 2014 (Magma) [NumberOfDivisors(2*n+1): n in [0..100]]; // Vincenzo Librandi, Mar 18 2015 (GAP) List([1..120], n->Tau(2*n-1)); # Muniru A Asiru, Dec 21 2018 CROSSREFS Bisection of A000005. Cf. A000005, A001620, A099777. Cf. A005408, A008438. Sequence in context: A175778 A357039 A226182 * A305973 A290978 A142240 Adjacent sequences: A099771 A099772 A099773 * A099775 A099776 A099777 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 October 1 14:54 EDT 2023. Contains 365826 sequences. (Running on oeis4.)