A141547 Numbers n whose abundance is 16.

550, 748, 1504, 7192, 7912, 10792, 17272, 30592, 1713592, 4526272, 8353792, 9928792, 11547352, 17999992, 89283592, 173482552, 361702144, 1081850752, 1845991216, 2146926592, 11097907192, 12985220152, 21818579968, 34357510144, 109170719992, 228354264064, 279632332792, 549746900992

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2008

Keywords

• nonn

Comments

Any term x of this sequence can be combined with any term y of A125248 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

a(41) > 10^18 - Hiroaki Yamanouchi, Aug 23 2018

Examples

			a(1) = 550, since sigma(550) - 2*550 = 1116 - 1100 = 16. - _Timothy L. Tiffin_, Sep 13 2016
		

Links

• Giovanni Resta and Hiroaki Yamanouchi, Table of n, a(n) for n = 1..40 (terms a(1)-a(32) from _Giovanni Resta_)

Crossrefs

Cf. A125248 (deficiency 16).

Programs

Magma

[n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 16]; // Vincenzo Librandi, Sep 14 2016

Mathematica

lst={}; Do[If[n==Plus@@Divisors[n]-n-16, AppendTo[lst,n]], {n,10^4}]; Print[lst];
lst = {}; Do[ If[2 n + 16 == DivisorSigma[1, n], AppendTo[lst, n]], {n, 10^8}]; lst (* Robert G. Wilson v, Aug 17 2008 *)
Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == 16 &] (* Vincenzo Librandi, Sep 14 2016 *)

PARI

is(n)=sigma(n)==2*n+16 \\ Charles R Greathouse IV, Feb 21 2017

Extensions

a(9)-a(14) from Robert G. Wilson v, Aug 17 2008

a(15)-a(24) from Donovan Johnson, Dec 21 2008

a(25)-a(28) from Donovan Johnson, Dec 08 2011