A141546 Numbers whose abundance is 14.

272, 7232, 30848, 516608, 134094848, 2146992128, 35184309174272

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2008

Keywords

• nonn
• more

Comments

a(7) > 10^12. - Donovan Johnson, Dec 08 2011

a(7) > 10^13. - Giovanni Resta, Mar 29 2013

a(8) > 10^18. - Hiroaki Yamanouchi, Aug 23 2018

Any term x of this sequence can be combined with any term y of A141550 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

Every number of the form 2^(j-1)*(2^j - 15), where 2^j - 15 is prime (see A059612), is a term. - Jon E. Schoenfield, Jun 02 2019

Examples

			a(1) = 272, since sigma(272) - 2*272 = 558 - 544 = 14. - _Timothy L. Tiffin_, Sep 13 2016
		

Crossrefs

Cf. A141550 (deficiency 14), A141545 (abundance 12), A141547 (abundance 16).

Programs

Magma

[n: n in [1..10^8] | SumOfDivisors(n)- 2*n eq 14]; // Vincenzo Librandi, Mar 20 2015

Mathematica

lst={};Do[If[n==Plus@@Divisors[n]-n-14,AppendTo[lst,n]],{n,10^4}];Print[lst];
lst = {}; Do[ If[2 n + 14 == DivisorSigma[1, n], AppendTo[lst, n]], {n, 2 10^8, 2}]; lst (* Robert G. Wilson v, Aug 17 2008 *)

PARI

isok(n) = sigma(n) - 2*n == 14; \\ Michel Marcus, Mar 20 2015

Formula

{k: A033880(k) = 14}. - R. J. Mathar, Jun 06 2024

Extensions

a(5)-a(6) from Donovan Johnson, Dec 21 2008

a(7) from Hiroaki Yamanouchi, Aug 23 2018