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A369066 Dirichlet convolution of Liouville's lambda (A008836) with A083345, as reordered by the Doudna sequence.

%I A369066 #11 Jan 17 2024 12:42:44
%S A369066 0,1,1,0,1,3,1,3,1,5,6,0,1,2,0,-1,1,7,8,0,10,14,5,8,1,2,3,0,2,0,4,6,1,
%T A369066 11,12,0,14,20,7,14,16,34,44,0,7,9,0,-3,1,2,3,0,5,5,2,5,2,6,8,0,2,7,1,
%U A369066 -3,1,13,14,0,16,32,11,20,18,54,68,0,11,13,0,-5,22,76,92,0,124,92,34,36,11,13,20,0,16
%N A369066 Dirichlet convolution of Liouville's lambda (A008836) with A083345, as reordered by the Doudna sequence.
%H A369066 Antti Karttunen, <a href="/A369066/b369066.txt">Table of n, a(n) for n = 0..16384</a>
%F A369066 a(n) = A369069(A005940(1+n)).
%o A369066 (PARI)
%o A369066 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A369066 A008836(n) = ((-1)^bigomega(n));
%o A369066 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A369066 A369069(n) = sumdiv(n,d,A008836(n/d)*A083345(d));
%o A369066 A369066(n) = A369069(A005940(1+n));
%Y A369066 Cf. A005940, A008836, A083345, A369067 (rgs-transform), A369069.
%Y A369066 Cf. also A366803 (compare the scatter plots).
%K A369066 sign,look
%O A369066 0,6
%A A369066 _Antti Karttunen_, Jan 16 2024