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
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
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