cp's OEIS Frontend

A229344 Mertens's function of the arithmetic derivative of n: a(n) = M(n'), a(1) = 0.

%I A229344 #51 Feb 25 2018 09:53:59
%S A229344 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,
%T A229344 -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,
%U A229344 -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
%N A229344 Mertens's function of the arithmetic derivative of n: a(n) = M(n'), a(1) = 0.
%C A229344 a(1) = 0 by convention. - _Antti Karttunen_, Nov 01 2017
%H A229344 Antti Karttunen, <a href="/A229344/b229344.txt">Table of n, a(n) for n = 1..16384</a>
%F A229344 a(1) = 0 and for n > 1, a(n) = A002321(A003415(n)).
%e A229344 For n=4, M(n') = M(4') = M(4) = -1.
%e A229344 For n=7, M(n') = M(7') = M(1) = 1.
%t A229344 Array[Total@ Map[MoebiusMu, Range@ If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]]] &, 89] (* _Michael De Vlieger_, Nov 01 2017 *)
%o A229344 (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];));}
%o A229344 a(n) = mertens(rd(n)); \\ _Michel Marcus_, Sep 24 2013
%o A229344 (PARI)
%o A229344 A002321(n) = sum(k=1, n, moebius(k));
%o A229344 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
%o A229344 A229344(n) = if(1==n,0,A002321(A003415(n))); \\ _Antti Karttunen_, Nov 01 2017
%Y A229344 Cf. A002321, A003415, A229340, A229341, A229342, A229343.
%K A229344 sign
%O A229344 1,6
%A A229344 _Luca Brigada Villa_, Sep 24 2013
%E A229344 Description and formula clarified and more terms added by _Antti Karttunen_, Nov 01 2017