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A132585
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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.
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3
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OFFSET
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1,1
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COMMENTS
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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]
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LINKS
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Table of n, a(n) for n=1..6.
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EXAMPLE
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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)
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MAPLE
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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);
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CROSSREFS
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Cf. A002961, A058072, A058073, A132586.
Sequence in context: A146641 A171590 A056981 * A049228 A076637 A040600
Adjacent sequences: A132582 A132583 A132584 * A132586 A132587 A132588
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KEYWORD
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hard,more,nonn
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AUTHOR
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Paolo P. Lava and Giorgio Balzarotti, Aug 23 2007
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EXTENSIONS
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a(6) from Donovan Johnson, Aug 31 2008
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STATUS
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approved
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