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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 (list; graph; refs; listen; history; text; internal format)
 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] LINKS 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: A146641 A171590 A056981 * A049228 A076637 A040600 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

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Last modified May 25 20:22 EDT 2013. Contains 225649 sequences.