%I #19 Jun 25 2021 22:50:47
%S 0,-1,-1,1,-1,0,-1,1,1,2,-1,-4,-1,4,-3,1,-1,-3,-1,-2,-1,2,-1,0,-6,-6,
%T 1,0,-1,6,-1,1,3,-6,-4,-2,-1,-6,5,0,-1,6,-1,4,3,-6,-1,-8,-8,7,-3,6,-1,
%U 6,4,-8,-1,-6,-1,12,-1,-6,3,1,8,-12,-1,10,3,-4,-1,-9,-1,-6,3,12,1
%N Third coefficient of the lindep transform of sigma(n).
%C If b(n) is a sequence of integers, we will call the "lindep transform" of b(n) the triplet of sequences (x(n), y(n), z(n)) such that:
%C (i) x(n) >= 1
%C (ii) x(n) + abs(y(n)) + abs(z(n)) is minimal
%C (iii) x(n)*b(n) + y(n)*n + z(n) = 0
%C (iv) if more than one triplet (x(n), y(n), z(n)) satisfies conditions (i), (ii), and (iii), we then choose the one with minimal y(n).
%C We call x(n) the first coefficient of the lindep transform of b(n), y(n) the second and z(n) the third. As this corresponds to the lindep function of PARI/GP this transform is called "lindep transform".
%H Benoit Cloitre, <a href="/A339792/a339792.png">a(n)/sqrt(n) every 1000 up to 6*10^6</a>
%F Conjecture: a(n) << sqrt(n) with -infinity < liminf_{n->infinity} a(n)/sqrt(n) < 0 and 0 < limsup_{n->infinity} a(n)/sqrt(n) < infinity exist (see graphic).
%Y Cf. A000203, A339790, A339791.
%K sign
%O 1,10
%A _Benoit Cloitre_, Dec 17 2020
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