The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A133700 A051731 * A001227; a(n) = Sum_{d|n} A001227(d). 4
 1, 2, 3, 3, 3, 6, 3, 4, 6, 6, 3, 9, 3, 6, 9, 5, 3, 12, 3, 9, 9, 6, 3, 12, 6, 6, 10, 9, 3, 18, 3, 6, 9, 6, 9, 18, 3, 6, 9, 12, 3, 18, 3, 9, 18, 6, 3, 15, 6, 12, 9, 9, 3, 20, 9, 12, 9, 6, 3, 27, 3, 6, 18, 7, 9, 18, 3, 9, 9, 18, 3, 24, 3, 6, 18, 9, 9, 18, 3, 15, 15, 6, 3, 27, 9, 6, 9, 12, 3, 36, 9, 9, 9 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA Inverse MÃ¶bius transform of A001227, the number of odd divisors of n. Row sums of triangle A133699. Dirichlet g.f. (zeta(s))^3*(1-1/2^s). - R. J. Mathar, Feb 07 2011 a(n) = Sum_{d|n} A001227(d). - Antti Karttunen, Sep 27 2018 Sum_{k=1..n} a(k) ~ n/4 * (log(n)^2 + (6*g - 2 + 2*log(2))*log(n) + 2 + 6*g^2 - log(2)^2 - 2*log(2) + 6*g*(log(2) - 1) - 6*sg1), where g is the Euler-Mascheroni constant A001620 and sg1 is the first Stieltjes constant A082633. - Vaclav Kotesovec, Feb 02 2019 G.f.: Sum_{k>=1} tau(k)*x^k/(1 - x^(2*k)), where tau = A000005. - Ilya Gutkovskiy, Sep 13 2019 EXAMPLE a(4) = sum of row 4 terms of triangle A133699: (1 + 1 + 0 + 1) = (1, 1, 0, 1) dot (1, 1, 2, 1), where A001227 = (1, 1, 2, 1, 2, 2, 2, 1, 3,...). PROG (PARI) A133700(n) = sumdiv(n, d, numdiv(d>>valuation(d, 2))); \\ Antti Karttunen, Sep 27 2018 CROSSREFS Cf. A000005, A001227, A051731, A133699. Sequence in context: A126868 A134187 A078644 * A087688 A126854 A115206 Adjacent sequences:  A133697 A133698 A133699 * A133701 A133702 A133703 KEYWORD nonn,mult AUTHOR Gary W. Adamson, Sep 21 2007 EXTENSIONS More terms from R. J. Mathar, Jan 19 2009 Second, equivalent formula added to the definition by Antti Karttunen, Sep 27 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 27 21:21 EDT 2021. Contains 346316 sequences. (Running on oeis4.)