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A339792
Third coefficient of the lindep transform of sigma(n).
3
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, 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, 6, 4, -8, -1, -6, -1, 12, -1, -6, 3, 1, 8, -12, -1, 10, 3, -4, -1, -9, -1, -6, 3, 12, 1
OFFSET
1,10
COMMENTS
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:
(i) x(n) >= 1
(ii) x(n) + abs(y(n)) + abs(z(n)) is minimal
(iii) x(n)*b(n) + y(n)*n + z(n) = 0
(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).
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".
FORMULA
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).
CROSSREFS
KEYWORD
sign
AUTHOR
Benoit Cloitre, Dec 17 2020
STATUS
approved