The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A229344 Mertens's function of the arithmetic derivative of n: a(n) = M(n'), a(1) = 0. 3
 0, 1, 1, -1, 1, -2, 1, -2, -1, -2, 1, -1, 1, -2, -2, -4, 1, -2, 1, -2, -1, -3, 1, -3, -1, -1, -1, -4, 1, -4, 1, -4, -2, -3, -2, -1, 1, -2, -1, -2, 1, -1, 1, -3, 0, -2, 1, -4, -2, -3, -3, -2, 1, -4, -1, -1, -1, -4, 1, -1, 1, -3, -2, -5, -2, -2, 1, -3, -1, -1, 1, -1, 1, 0, -2, -4, -2, -3, 1, -4, -3, -3, 1, -1, -1, -3, -4, -4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS a(1) = 0 by convention. - Antti Karttunen, Nov 01 2017 LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(1) = 0 and for n > 1, a(n) = A002321(A003415(n)). EXAMPLE For n=4, M(n') = M(4') = M(4) = -1. For n=7, M(n') = M(7') = M(1) = 1. MATHEMATICA Array[Total@ Map[MoebiusMu, Range@ If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]]] &, 89] (* Michael De Vlieger, Nov 01 2017 *) PROG (PARI) rd(n) = {local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]; )); } a(n) = mertens(rd(n)); \\ Michel Marcus, Sep 24 2013 (PARI) A002321(n) = sum(k=1, n, moebius(k)); A003415(n) = { my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From Michael B. Porter, Nov 25 2009 A229344(n) = if(1==n, 0, A002321(A003415(n))); \\ Antti Karttunen, Nov 01 2017 CROSSREFS Cf. A002321, A003415, A229340, A229341, A229342, A229343. Sequence in context: A306446 A100387 A322869 * A210501 A307781 A356112 Adjacent sequences: A229341 A229342 A229343 * A229345 A229346 A229347 KEYWORD sign AUTHOR Luca Brigada Villa, Sep 24 2013 EXTENSIONS Description and formula clarified and more terms added by Antti Karttunen, Nov 01 2017 STATUS approved

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

Last modified June 18 15:47 EDT 2024. Contains 373481 sequences. (Running on oeis4.)