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%I #41 Sep 08 2022 08:45:35
%S 13,45,76,688,8896,133888,537051136,35184418226176,144115191028645888
%N Numbers n whose deficiency is 12: 2n - sigma(n) = 12.
%C Numbers n whose abundance is -12. No other terms up to n=100,000,000. - _Jason G. Wurtzel_, Aug 24 2010
%C a(8) > 10^12. - _Donovan Johnson_, Dec 08 2011
%C a(8) > 10^13. - _Giovanni Resta_, Mar 29 2013
%C a(10) > 10^18. - _Hiroaki Yamanouchi_, Aug 21 2018
%C a(8) <= 35184418226176 = 3.52*10^13. Indeed, for all k in A102633, the number 2^(k-1)*(2^k+11) is in this sequence. So far all terms except a(2) are of this form. For k = 23, this gives the (probably next) term 35184418226176. For k = 29, 31, 55, 71, ... this yields 144115191028645888, 2305843021024854016, 649037107316853651724695645454336, 2787593149816327892704951291908936712585216, ... which are also in this sequence. - _M. F. Hasler_, Apr 23 2015
%C Any term x = a(m) can be combined with any term y = A141545(n) to satisfy the property (sigma(x)+sigma(y))/(x+y) = 2. Although this property is a necessary condition for two numbers to be amicable, it is not a sufficient one. So far, these two sequences have not produced an amicable pair. However, if one is ever found, then it will exhibit x-y = 12. - _Timothy L. Tiffin_, Sep 13 2016
%e a(1) = 13, since 2*13 - sigma(13) = 26 - 14 = 12. - _Timothy L. Tiffin_, Sep 13 2016
%t lst={};Do[If[n==Plus@@Divisors[n]-n+12,AppendTo[lst,n]],{n,10^4}];Print[lst];
%t Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == - 12 &] (* _Vincenzo Librandi_, Sep 14 2016 *)
%o (PARI) for(n=1, 10^8, if(((sigma(n)-2*n)==-12), print1(n, ", "))) \\ _Jason G. Wurtzel_, Aug 24 2010
%o (Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -12]; // _Vincenzo Librandi_, Sep 14 2016
%Y Cf. A000203, A033880, A005100; A191363 (deficiency 2), A125246 (deficiency 4), A141548 (deficiency 6), A125247 (deficiency 8), A101223 (deficiency 10), A141550 (deficiency 14), A125248 (deficiency 16), A223608 (deficiency 18), A223607 (deficiency 20); A141545 (abundance 12).
%K nonn,hard,more
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Aug 16 2008
%E a(7) from _Donovan Johnson_, Dec 08 2011
%E a(8)-a(9) from _Hiroaki Yamanouchi_, Aug 21 2018
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