A131038 - OEIS

A131038

a(1)=1. For n >= 2, Sum_{k|n, neither (k+1) nor (k-1) divides n} a(k) = 0. (The sum is over the isolated divisors of n. A divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.).

1, 0, -1, 0, -1, 0, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, -1, 1, 1, -1, 0, 0, 1, 0, 0, -1, -2, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, -1, -2, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 1, -1, 1, 1, -1, 1, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, 0, -1, 1, 0, 0, 1, -1, -1, 0, 0, 1, -1, 0, 1, 1, 1, 0, -1, 1, 1, 0, 1, 1, 1, 0, -1, 0, 0, 0, -1, -1, -1, 0, -1, 1, -1, 0, -1

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OFFSET

1,30

COMMENTS

The value of a(2) is arbitrary. If a(2) is any number and the rest of the sequence remains unchanged, then the sum over isolated divisors still always equals 0 for all n >= 2.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

EXAMPLE

The positive divisors of 30 are 1,2,3,5,6,10,15,30. Of these, 1,2,3 are adjacent and 5 and 6 are adjacent. So the isolated divisors of 30 are 10,15,30. Therefore a(30) is such that a(10)+a(15)+a(30) = 1 +1 +a(30) =0. So a(30) = -2.

PROG

(PARI) A131038(n) = if(n<=2, 2-n, -((n%2)+sumdiv(n, d, if((d<n)&&(d>2)&&(n%(d-1))&&(n%(d+1)), A131038(d), 0)))); \\ Antti Karttunen, Apr 06 2021

CROSSREFS

Cf. A008683, A132881.

Sequence in context: A016427 A326170 A243841 * A016353 A016398 A024359

Adjacent sequences: A131035 A131036 A131037 * A131039 A131040 A131041

KEYWORD

sign

AUTHOR

Leroy Quet, Sep 23 2007

EXTENSIONS

Extended by Ray Chandler, Jun 25 2008

STATUS

approved