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.

8, 24, 8925, 32445, 118540859325

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: A037025 A105063 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