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A088012 Odd solutions to Abs[sigma[x]-2x]<=log[x]. Numbers n whose abundance-radius does not exceed log[n]. 16
1155, 8925, 32445, 442365, 159030135, 815634435, 2586415095 (list; graph; refs; listen; history; internal format)
OFFSET

1,1

COMMENTS

This sequence should include odd perfect numbers too, if they exist.

There are no other terms below 2*10^9.

..Abundancy(n)..............n.............2n.......sigma(n)..difference

1.99480519480519.........1155...........2310...........2304.........-.6

2.00067226890756.........8925..........17850..........17856...........6

2.00018492834027........32445..........64890..........64896...........6

2.00001356346004.......442365.........884730.........884736...........6

2.00000011318610....159030135......318060270......318060288..........18

1.99999999264376....815634435.....1631268870.....1631268864.........-.6

As it happens, abundance-radius of these is -6, 6 or 18. This is not necessarily true for larger terms.

LINKS

Walter Nissen, Home Page (listed in lieu of email address)

EXAMPLE

1155 is in the sequence because sigma ( 1155 ) = 2304, giving 2*1155 - 2304 = 6, while natural log of 1155 is about 7.05.

MATHEMATICA

abu[x_] := Abs[DivisorSigma[1, x]-2*x] Do[If[ !Greater[abu[n], Log[n]//N]&&OddQ[n], Print[n]], {n, 1, 100000}]

CROSSREFS

Cf. A088007-A088011, A077374, A005100, A005101, A000079, A087167, A000079, A000396.

Sequence in context: A185689 A046390 A147577 * A046406 A136355 A157168

Adjacent sequences:  A088009 A088010 A088011 * A088013 A088014 A088015

KEYWORD

hard,nonn

AUTHOR

Labos E. (labos(AT)ana.sote.hu) and Farideh Firoozbakht (f.firoozbakht(AT)sci.ui.ac.ir), Oct 20 2003

EXTENSIONS

Additional comments from Walter Nissen Dec 15 2005

a(7) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Dec 21 2008

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Last modified February 17 10:05 EST 2012. Contains 206009 sequences.