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

1,1

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

Links

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

Example

a(1) = 550, since sigma(550) - 2*550 = 1116 - 1100 = 16. - Timothy L. Tiffin, Sep 13 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 *)

Prog

(Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 16]; // Vincenzo Librandi, Sep 14 2016
(PARI) is(n)=sigma(n)==2*n+16 \\ Charles R Greathouse IV, Feb 21 2017

Crossrefs

Cf. A125248 (deficiency 16).

Sequence in context: A235585 A210399 A232314 * A236723 A189502 A190075

Adjacent sequences: A141544 A141545 A141546 * A141548 A141549 A141550

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Aug 16 2008

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

Status

approved