A141550 Numbers n whose deficiency is 14.

27, 34, 232, 34432, 549762629632

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2008

Keywords

• nonn

Comments

a(6) > 10^12. - Donovan Johnson, Dec 08 2011

a(6) > 10^13. - Giovanni Resta, Mar 29 2013

a(6) > 10^18. - Hiroaki Yamanouchi, Aug 21 2018

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

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

Examples

			a(1) = 27, since 2*27 - sigma(27) = 54 - 40 = 14. - _Timothy L. Tiffin_, Sep 13 2016
		

Crossrefs

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).

Programs

Magma

[n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq -14]; // Vincenzo Librandi, Sep 14 2016

Mathematica

lst={};Do[If[n==Plus@@Divisors[n]-n+14,AppendTo[lst,n]],{n,10^4}];Print[lst];
Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == - 14 &] (* Vincenzo Librandi, Sep 14 2016 *)

Extensions

a(5) from Donovan Johnson, Dec 08 2011