1,1

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.

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

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

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

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

Sequence in context: A020382 A046390 A147577 this_sequence A046406 A136355 A157168

Adjacent sequences: A088009 A088010 A088011 this_sequence A088013 A088014 A088015

hard,nonn

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

Additional comments from Walter Nissen Dec 15 2005

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