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%I #10 Jul 11 2013 10:03:27
%S 25,49,799,899,32399,292681
%N 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.
%C 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?
%C a(7) <= 1492995736325809. [From _Donovan Johnson_, Aug 31 2008]
%C a(7) > 10^13. - _Giovanni Resta_, Jul 11 2013
%e n=25 -> sigma(25)= 1+5+25 -> sigma(n)-n-1=5
%e n+1=26 -> sigma(26)= 1+2+13+26 -> sigma(n+1)-n-2=2+13=15
%e 15/5 = 3 (integer > 0)
%p 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);
%Y Cf. A002961, A058072, A058073, A132586.
%K hard,more,nonn
%O 1,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Aug 23 2007
%E a(6) from _Donovan Johnson_, Aug 31 2008
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