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A132586
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Numbers n such that sigma(n+1)-n-2 divides sigma(n)-n-1, 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
| 1,1
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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?
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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)
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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);
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CROSSREFS
| Cf. A002961, A058072, A058073, A132585.
Sequence in context: A037025 A105063 A166483 * A103953 A076444 A023056
Adjacent sequences: A132583 A132584 A132585 * A132587 A132588 A132589
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KEYWORD
| hard,more,nonn
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Aug 23 2007
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EXTENSIONS
| a(5) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Aug 31 2008
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