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%I #25 Sep 08 2022 08:45:35
%S 27,34,232,34432,549762629632
%N Numbers n whose deficiency is 14.
%C a(6) > 10^12. - _Donovan Johnson_, Dec 08 2011
%C a(6) > 10^13. - _Giovanni Resta_, Mar 29 2013
%C a(6) > 10^18. - _Hiroaki Yamanouchi_, Aug 21 2018
%C a(6) <= b(38) = 37778931864743868104704 = 3.77789*10^22, since b(k) = 2^(k-1)*(2^k+13) is in this sequence for all k in A102634, i.e., 2^k+13 is prime. All known terms except a(1) = 27 are of this form: a(2..5) = b(k) with k = 2, 4, 8, 20, and k = 38 yields the next larger term of this form. - _M. F. Hasler_, Jul 18 2016
%C Any term x of this sequence can be combined with any term y of A141546 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
%e a(1) = 27, since 2*27 - sigma(27) = 54 - 40 = 14. - _Timothy L. Tiffin_, Sep 13 2016
%t lst={};Do[If[n==Plus@@Divisors[n]-n+14,AppendTo[lst,n]],{n,10^4}];Print[lst];
%t Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == - 14 &] (* _Vincenzo Librandi_, Sep 14 2016 *)
%o (Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -14]; // _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), A141549 (deficiency 12), A125248 (deficiency 16); A141546 (abundance 14).
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Aug 16 2008
%E a(5) from _Donovan Johnson_, Dec 08 2011
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