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Numbers n whose abundance is 16.
8

%I #29 Sep 08 2022 08:45:35

%S 550,748,1504,7192,7912,10792,17272,30592,1713592,4526272,8353792,

%T 9928792,11547352,17999992,89283592,173482552,361702144,1081850752,

%U 1845991216,2146926592,11097907192,12985220152,21818579968,34357510144,109170719992,228354264064,279632332792,549746900992

%N Numbers n whose abundance is 16.

%C 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

%C a(41) > 10^18 - _Hiroaki Yamanouchi_, Aug 23 2018

%H Giovanni Resta and Hiroaki Yamanouchi, <a href="/A141547/b141547.txt">Table of n, a(n) for n = 1..40</a> (terms a(1)-a(32) from _Giovanni Resta_)

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

%t lst={}; Do[If[n==Plus@@Divisors[n]-n-16, AppendTo[lst,n]], {n,10^4}]; Print[lst];

%t lst = {}; Do[ If[2 n + 16 == DivisorSigma[1, n], AppendTo[lst, n]], {n, 10^8}]; lst (* _Robert G. Wilson v_, Aug 17 2008 *)

%t Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == 16 &] (* _Vincenzo Librandi_, Sep 14 2016 *)

%o (Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 16]; // _Vincenzo Librandi_, Sep 14 2016

%o (PARI) is(n)=sigma(n)==2*n+16 \\ _Charles R Greathouse IV_, Feb 21 2017

%Y Cf. A125248 (deficiency 16).

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Aug 16 2008

%E a(9)-a(14) from _Robert G. Wilson v_, Aug 17 2008

%E a(15)-a(24) from _Donovan Johnson_, Dec 21 2008

%E a(25)-a(28) from _Donovan Johnson_, Dec 08 2011