A339792 Third coefficient of the lindep transform of sigma(n).

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".

Links

Table of n, a(n) for n=1..77.

Benoit Cloitre, a(n)/sqrt(n) every 1000 up to 6*10^6

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

Cf. A000203, A339790, A339791.

Sequence in context: A229340 A322968 A072721 * A285711 A035092 A160598

Adjacent sequences: A339789 A339790 A339791 * A339793 A339794 A339795

Keyword

sign

Author

Benoit Cloitre, Dec 17 2020

Status

approved