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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.
3
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
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
KEYWORD
hard,more,nonn
AUTHOR
EXTENSIONS
a(6) from Donovan Johnson, Aug 31 2008
STATUS
approved