A088833 Numbers n whose abundance is 8: sigma(n) - 2n = 8.

56, 368, 836, 11096, 17816, 45356, 77744, 91388, 128768, 254012, 388076, 2087936, 2291936, 13174976, 29465852, 35021696, 45335936, 120888092, 260378492, 381236216, 775397948, 3381872252, 4856970752, 6800228816, 8589344768, 44257207676, 114141404156

Offset: 1

Author

Labos Elemer, Oct 28 2003

Keywords

• nonn

Comments

A subset of A045770.

If p=2^m-9 is prime (m is in the sequence A059610) then n=2^(m-1)*p is in the sequence. See comment lines of the sequence A088831. 56, 368, 128768, 2087936 & 8589344768 are of the mentioned form. - Farideh Firoozbakht, Feb 15 2008

a(28) > 10^12. - Donovan Johnson, Dec 08 2011

a(31) > 10^13. - Giovanni Resta, Mar 29 2013

a(38) > 10^18. - Hiroaki Yamanouchi, Aug 23 2018

Any term x of this sequence can be combined with any term y of A125247 to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2, which is a necessary (but not sufficient) condition for two numbers to be amicable. - Timothy L. Tiffin, Sep 13 2016

Examples

			Except first 4 terms of A045770 (1, 7, 10, and 49) are here: abundances = {-1,-6,-2,-41,8,8,8,8,8,8,8,8,8,8,8,8,8}.
		

Links

• Giovanni Resta and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..37 (terms a(1)-a(30) from _Giovanni Resta_)

Crossrefs

Cf. A033880, A045668, A045669, A045770, A088831, A088832, A059610, A125247 (deficiency 8).

Programs

Mathematica

Do[If[DivisorSigma[1,n]==2n+8,Print[n]],{n,100000000}] (* Farideh Firoozbakht, Feb 15 2008 *)

PARI

is(n)=sigma(n)==2*n+8 \\ Charles R Greathouse IV, Feb 21 2017

Extensions

a(14)-a(17) from Farideh Firoozbakht, Feb 15 2008

a(18)-a(25) from Donovan Johnson, Dec 23 2008

a(26)-a(27) from Donovan Johnson, Dec 08 2011