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 A129628 Inverse Moebius transform of A001511. 4
 1, 3, 2, 6, 2, 6, 2, 10, 3, 6, 2, 12, 2, 6, 4, 15, 2, 9, 2, 12, 4, 6, 2, 20, 3, 6, 4, 12, 2, 12, 2, 21, 4, 6, 4, 18, 2, 6, 4, 20, 2, 12, 2, 12, 6, 6, 2, 30, 3, 9, 4, 12, 2, 12, 4, 20, 4, 6, 2, 24, 2, 6, 6, 28, 4, 12, 2, 12, 4, 12, 2, 30, 2, 6, 6, 12, 4, 12, 2, 30, 5, 6, 2, 24, 4, 6, 4, 20 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Andrew Howroyd) FORMULA a(2n) = a(n) + A000005(2n), a(2n+1) = A000005(2n+1). Dirichlet g.f.: zeta(s)^2 * 2^s/(2^s-1). - Ralf Stephan, Jun 17 2007, corrected by Vaclav Kotesovec, Feb 02 2019 a(n) = Sum_{d|n} A001511(d). - Andrew Howroyd, Aug 04 2018 Sum_{k=1..n} a(k) ~ 2*n * (2*gamma - 1 + log(n/2)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Feb 02 2019 Multiplicative with a(2^e) = (e+1)*(e+2)/2, and a(p^e) = e+1 for p > 2. - Amiram Eldar, Sep 30 2020 MATHEMATICA f[p_, e_] := If[p==2, (e+1)*(e+2)/2, e+1]; a[1] = 1; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 30 2020 *) PROG (PARI) a(n)={sumdiv(n, d, 1 + valuation(d, 2))} \\ Andrew Howroyd, Aug 04 2018 CROSSREFS Row sums of A129353. Cf. A000005, A001511, A001620, A129628. Sequence in context: A021758 A040008 A129354 * A245691 A071044 A077066 Adjacent sequences:  A129625 A129626 A129627 * A129629 A129630 A129631 KEYWORD nonn,mult,easy AUTHOR Ralf Stephan, May 31 2007 STATUS approved

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Last modified May 14 05:45 EDT 2021. Contains 343872 sequences. (Running on oeis4.)