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A369068 Möbius transform of A083345, where A083345(n) = n' / gcd(n,n'), and n' stands for the arithmetic derivative of n, A003415.

%I A369068 #8 Jan 16 2024 12:12:09
%S A369068 0,1,1,0,1,3,1,2,1,5,1,-1,1,7,6,-1,1,1,1,-1,8,11,1,5,1,13,-1,-1,1,14,
%T A369068 1,3,12,17,10,-1,1,19,14,9,1,20,1,-1,4,23,1,-3,1,1,18,-1,1,-3,14,13,
%U A369068 20,29,1,-6,1,31,6,-2,16,32,1,-1,24,34,1,1,1,37,2,-1,16,38,1,-5,3,41,1,-8,20,43,30,21,1,4,18
%N A369068 Möbius transform of A083345, where A083345(n) = n' / gcd(n,n'), and n' stands for the arithmetic derivative of n, A003415.
%C A369068 In contrast to A346485, this sequence has also negative values. Compare also to A369069.
%H A369068 Antti Karttunen, <a href="/A369068/b369068.txt">Table of n, a(n) for n = 1..16384</a>
%F A369068 a(n) = Sum_{d|n} A008683(n/d) * A083345(d).
%o A369068 (PARI)
%o A369068 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A369068 A369068(n) = sumdiv(n,d,moebius(n/d)*A083345(d));
%Y A369068 Cf. A003415, A008683, A083345.
%Y A369068 Cf. also A346485, A369069.
%K A369068 sign
%O A369068 1,6
%A A369068 _Antti Karttunen_, Jan 16 2024