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, 2361183241263023915008, 865268370658615254581248

Offset

1,1

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 2659081164473524666156036569407474433465812408221914992167761215488 = 2^63 * 18446744095482502937 * 15628674417636146874732718453. - Max Alekseyev, Aug 29 2025

14522710167900405545492917671385291559503626125198828394930119586292951687001113692109441374243337137942822752616448 = 2^119 * 1329228103263100697187241790184084113 * 16439124000186855960847939730903837101346317 is a term. - Alexander Violette, Nov 01 2025

Links

Table of n, a(n) for n=1..18.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Subsequence of A045769.

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

Sequence in context: A101097 A067702 A163193 * A366748 A198311 A385976

Adjacent sequences: A088829 A088830 A088831 * A088833 A088834 A088835

Keyword

nonn,more

Author

Labos Elemer, Oct 28 2003

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)-a(17) from Max Alekseyev, Sep 02 2025

a(18) from Max Alekseyev, Jan 27 2026

Status

approved