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A339791 Second coefficient of the lindep transform of sigma(n). 3
-1, -1, -1, -2, -1, -2, -1, -2, -3, -2, -1, -2, -1, -2, -3, -2, -1, -2, -1, -2, -3, -5, -1, -5, -1, -3, -3, -2, -1, -5, -1, -2, -3, -3, -4, -5, -1, -3, -3, -9, -1, -7, -1, -2, -7, -3, -1, -5, -1, -2, -7, -2, -1, -9, -4, -2, -7, -3, -1, -3, -1, -3, -5, -2, -4, -2, -1, -2, -7, -2, -1, -8, -1, -3, -5, -2, -5, -2, -1, -7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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 as:

(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 with the conditions (i), (ii), (iii) there exist several triplets (x(n), y(n), z(n)) 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..80.

Benoit Cloitre, a(n)/sqrt(n) every 1000 up to 6.10^6

FORMULA

Conjecture: a(n) << sqrt(n) with -infty < liminf n--> infty a(n)/sqrt(n) < 0 exists (see graphic). Trivially limsup a(n)/sqrt(n) = 0 since for prime n we have a(n)=-1.

PROG

(PARI) a(n)=(lindep([sigma(n), n, 1])*sign(lindep([sigma(n), n, 1])[1]))[2]

CROSSREFS

Cf. A000203, A339790, A339792.

Sequence in context: A082061 A327979 A107286 * A087039 A102096 A322813

Adjacent sequences:  A339788 A339789 A339790 * A339792 A339793 A339794

KEYWORD

sign

AUTHOR

Benoit Cloitre, Dec 17 2020

STATUS

approved

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Last modified October 27 09:55 EDT 2021. Contains 348274 sequences. (Running on oeis4.)