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.

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: A107557 A020382 A046390 this_sequence A046406 A136355 A062915

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 (wnissen(AT)tfn.net), Dec 15 2005