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A132586 Numbers n such that sigma(n+1)-n-2 divides sigma(n)-n-1, where sigma(n) is sum of positive divisors of n and the ratio is greater than zero. 3
8, 24, 8925, 32445, 118540859325 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The banal case of ratio equal to zero is excluded. In fact if n is a prime than sigma(n)-n-1=0. Therefore the ratio with sigma(n+1)-n-2 is equal to zero. Is this sequence finite?

a(6), if it exists, is larger than 10^13. - Giovanni Resta, Jul 13 2015

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

n=8 -> sigma(8)=1+2+4+8 -> sigma(n)-n-1=2+4=6.

n+1=9 -> sigma(9)=1+3+9 -> sigma(n+1)-n-2=3.

6/3 = 2 (integer >0)

MAPLE

with(numtheory); P:=proc(n) local a, i; for i from 1 by 1 to n do if sigma(i+1)-i-2>0 then a:=(sigma(i)-i-1)/(sigma(i+1)-i-2); if a>0 and trunc(a)=a then print(i); fi; fi; od; end: P(100000);

CROSSREFS

Cf. A002961, A058072, A058073, A132585.

Sequence in context: A105063 A166483 A274303 * A208400 A103953 A076444

Adjacent sequences:  A132583 A132584 A132585 * A132587 A132588 A132589

KEYWORD

hard,more,nonn

AUTHOR

Paolo P. Lava and Giorgio Balzarotti, Aug 23 2007

EXTENSIONS

a(5) from Donovan Johnson, Aug 31 2008

STATUS

approved

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Last modified April 16 04:49 EDT 2021. Contains 343030 sequences. (Running on oeis4.)