A223607 Numbers whose deficiency is 20: sigma(k) - 2*k = -20.

46, 154, 190, 2656, 6490, 44650, 318250, 1360810, 1503370, 1788490, 3214090, 103712410, 3915380170, 6077111050, 9796360330, 10828121356, 33086522327050, 35966517350410, 11577093570201610, 16726040141635450, 576460762503970816, 12635070132908018630656, 184488041886383491200010

Offset

1,1

Comments

Contains 2^(t-1)*(2^t+19) for t in A057221. - Max Alekseyev, Jan 22 2026

Any term x of this sequence can be combined with any term y of A223611 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

275662616397029416254228490, 22676188020687854193666634934837575690, 250702780414440783177905513094097920010, and 2831124349658085626574918972050788187735050 are terms of this sequence. - Alexander Violette, Dec 20 2025 and Apr 12 2026

Also contains 6944097377138312533769355550136284569610 and 642489841737594313369346857791485340812925092518774130638223539538231296. - Max Alekseyev, Jan 22 2026

Links

Table of n, a(n) for n=1..23.

Example

For k = 1360810, sigma(k)-2*k = -20.

Mathematica

Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == - 20 &] (* Vincenzo Librandi, Sep 14 2016 *)

Prog

(PARI) for(n=1, 10^8, if(sigma(n)-2*n==-20, print1(n ", ")))
(Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -20]; // Vincenzo Librandi, Sep 14 2016

Crossrefs

Cf. A000203, A033879, A057221, A191363, A223611 (abundance 20).

Sequence in context: A053019 A044378 A044759 * A189809 A350556 A251467

Adjacent sequences: A223604 A223605 A223606 * A223608 A223609 A223610

Keyword

nonn

Author

Donovan Johnson at suggestion of N. J. A. Sloane and Robert G. Wilson v, Mar 23 2013

Extensions

a(17)-a(21) from Hiroaki Yamanouchi, Aug 21 2018

a(22)-a(23) from Alexander Violette confirmed and added by Max Alekseyev, Feb 04 2026

Status

approved