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A223611 Numbers k whose abundance is 20: sigma(k) - 2*k = 20.

%I A223611 #28 Sep 08 2022 08:46:04
%S A223611 176,1376,3230,3770,6848,114256,125696,544310,561824,740870,2075648,
%T A223611 4199030,4607296,8436950,33468416,134045696,199272950,624032630,
%U A223611 1113445430,1550860550,85905593344,2199001235456,35184284008448,10805836895078390,103285638050111990
%N A223611 Numbers k whose abundance is 20: sigma(k) - 2*k = 20.
%C A223611 Suggested by _N. J. A. Sloane_ and _Robert G. Wilson v_.
%C A223611 a(22) > 10^12.
%C A223611 a(23) > 10^13. - _Giovanni Resta_, Mar 29 2013
%C A223611 a(29) > 10^18. - _Hiroaki Yamanouchi_, Aug 23 2018
%C A223611 Any term x of this sequence can be combined with any term y of A223607 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
%C A223611 Every number of the form 2^(j-1)*(2^j - 21), where 2^j - 21 is prime, is a term. - _Jon E. Schoenfield_, Jun 02 2019
%H A223611 Hiroaki Yamanouchi, <a href="/A223611/b223611.txt">Table of n, a(n) for n = 1..28</a>
%e A223611 For k = 544310, sigma(k) - 2*k = 20.
%t A223611 Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == 20 &] (* _Vincenzo Librandi_, Sep 14 2016 *)
%o A223611 (PARI) for(n=1, 10^8, if(sigma(n)-2*n==20, print1(n ", ")))
%o A223611 (Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 20]; // _Vincenzo Librandi_, Sep 14 2016
%Y A223611 Cf. A000203, A033880, A223607 (deficiency 20).
%K A223611 nonn
%O A223611 1,1
%A A223611 _Donovan Johnson_, Mar 23 2013
%E A223611 a(22) from _Giovanni Resta_, Mar 29 2013
%E A223611 a(23)-a(25) from _Hiroaki Yamanouchi_, Aug 23 2018