A088832 Numbers k whose abundance is 4: sigma(k) - 2*k = 4.

12, 70, 88, 1888, 4030, 5830, 32128, 521728, 1848964, 8378368, 34359083008, 66072609790, 549753192448, 259708613909470, 2251799645913088, 9223372026117357568

Offset: 1

Author

Labos Elemer, Oct 28 2003

Keywords

• nonn
• more

Comments

If 2^m-5 is prime (A059608) then n=2^(m-1)*(2^m-5) is in the sequence. 12, 88, 1888, 32128, 521728, 8378368 & 34359083008 are such terms. See comments in A088831. - Farideh Firoozbakht, Feb 15 2008

Any term x of this sequence can be combined with any term y of A125246 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

Also contains 865268370658615254581248 = 2^23 * 16823249 * 6131278669. - Max Alekseyev, May 29 2025

Examples

			Abundances of terms in A045769: {-5,4,4,4,4,4,4,4,4,4} so A045769(1)=9 is not here.
		

Crossrefs

Subsequence of A045769.

Cf. A033880, A045768, A088830, A059608, A125246 (deficiency 4).

Programs

Mathematica

Do[If[DivisorSigma[1,n]==2n+4,Print[n]],{n,650000000}] (* Farideh Firoozbakht, Feb 15 2008 *)

PARI

is(n)=sigma(n)==2*n+4 \\ Charles R Greathouse IV, Feb 21 2017

Formula

Solutions to sigma(x)-2*x=4.

Extensions

One more terms from Farideh Firoozbakht, Feb 15 2008

a(11)-a(12) from Donovan Johnson, Dec 23 2008

a(13) from Donovan Johnson, Dec 08 2011

a(14)-a(15) from Hiroaki Yamanouchi, Aug 23 2018

a(16) from Max Alekseyev, May 29 2025