A132585 Numbers n such that sigma(n)-n-1 divides sigma(n+1)-n-2, where sigma(n) is sum of positive divisors of n and the ratio is greater than zero.

25, 49, 799, 899, 32399, 292681

Offset

1,1

Comments

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

a(7) <= 1492995736325809. [From Donovan Johnson, Aug 31 2008]

a(7) > 10^13. - Giovanni Resta, Jul 11 2013

Links

Table of n, a(n) for n=1..6.

Example

n=25 -> sigma(25)= 1+5+25 -> sigma(n)-n-1=5
n+1=26 -> sigma(26)= 1+2+13+26 -> sigma(n+1)-n-2=2+13=15
15/5 = 3 (integer > 0)

Maple

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

Crossrefs

Cf. A002961, A058072, A058073, A132586.

Sequence in context: A171590 A322434 A056981 * A049228 A309828 A076637

Adjacent sequences: A132582 A132583 A132584 * A132586 A132587 A132588

Keyword

hard,more,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Aug 23 2007

Extensions

a(6) from Donovan Johnson, Aug 31 2008

Status

approved