A223610 - OEIS

%I #26 Sep 08 2022 08:46:04

%S 208,6976,8415,31815,351351,2077696,20487159,159030135,536559616,

%T 2586415095,137433972736,2199003332608

%N Numbers k whose abundance is 18: sigma(k) - 2*k = 18.

%C Suggested by _N. J. A. Sloane_ and _Robert G. Wilson v_.

%C a(12) > 10^12.

%C a(13) > 10^13. - _Giovanni Resta_, Mar 29 2013

%C a(13) > 10^18. - _Hiroaki Yamanouchi_, Aug 23 2018

%C Any term x of this sequence can be combined with any term y of A223608 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(13) <= 2305842988812599296. Every number of the form 2^(j-1)*(2^j - 19), where 2^j - 19 is prime, is a term. - _Jon E. Schoenfield_, Jun 02 2019

%e For k = 159030135, sigma(k) - 2*k = 18.

%t Select[Range[1, 10^8], DivisorSigma[1, #] - 2 # == 18 &] (* _Vincenzo Librandi_, Sep 14 2016 *)

%o (PARI) for(n=1, 10^8, if(sigma(n)-2*n==18, print1(n ", ")))

%o (Magma) [n: n in [1..9*10^6] | (SumOfDivisors(n)-2*n) eq 18]; // _Vincenzo Librandi_, Sep 14 2016

%Y Cf. A000203, A033880, A223608 (deficiency 18).

%K nonn,more

%O 1,1

%A _Donovan Johnson_, Mar 23 2013

%E a(12) from _Giovanni Resta_, Mar 29 2013