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!)
 A174238 Inverse Moebius transform of even part of n (A006519). 1
 1, 3, 2, 7, 2, 6, 2, 15, 3, 6, 2, 14, 2, 6, 4, 31, 2, 9, 2, 14, 4, 6, 2, 30, 3, 6, 4, 14, 2, 12, 2, 63, 4, 6, 4, 21, 2, 6, 4, 30, 2, 12, 2, 14, 6, 6, 2, 62, 3, 9, 4, 14, 2, 12, 4, 30, 4, 6, 2, 28, 2, 6, 6, 127, 4, 12, 2, 14, 4, 12, 2, 45, 2, 6, 6, 14, 4, 12, 2, 62 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A Dirichlet g.f. would be greatly appreciated. The Dirichlet g.f. is the Dirichlet g.f. of A006519 multiplied by zeta(s). - R. J. Mathar, Feb 06 2011 Multiplicative because A006519 is. - Andrew Howroyd, Jul 27 2018 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Andrew Howroyd) FORMULA a(1) = 1, a(2n) = 2a(n) + A001227(n), a(2n+1) = A000005(2n+1). Dirichlet g.f.:  zeta(s)^2*(1-2^(-s))/(1-2^(-s+1)). - Ralf Stephan, Mar 27 2015 Multiplicative with a(2^e) = 2^(e+1)-1, and a(p^e) = e+1 for p > 2. - Amiram Eldar, Sep 30 2020 MATHEMATICA a[n_] := Sum[2^IntegerExponent[d, 2], {d, Divisors[n]}]; Array[a, 80] (* Jean-François Alcover, Feb 16 2020, from PARI *) f[p_, e_] := If[p==2, 2^(e+1)-1, 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, 2^valuation(d, 2)); \\ Michel Marcus, Mar 27 2015 CROSSREFS Cf. A000005, A006519, A001227. Sequence in context: A302714 A193574 A209639 * A175920 A200593 A249112 Adjacent sequences:  A174235 A174236 A174237 * A174239 A174240 A174241 KEYWORD nonn,mult,easy AUTHOR Ralf Stephan, Nov 27 2010 EXTENSIONS Title corrected by R. J. Mathar, Feb 06 2011 Terms a(61) and beyond from Andrew Howroyd, Jul 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 August 2 02:53 EDT 2021. Contains 346409 sequences. (Running on oeis4.)