%I #42 Feb 18 2024 08:20:02
%S 4,8,32,128,8192,131072,524288,2147483648,2305843009213693952,
%T 618970019642690137449562112
%N Numbers k such that sigma(sigma(k) - k) = k.
%C Because numbers of the form 1+A000668(.) are a subsequence, 162259276829213363391578010288128 and 170141183460469231731687303715884105728 are also in the sequence (not necessarily the next ones). - _Joerg Arndt_, Jul 01 2012
%F a(n) = 1 + A000668(n) (conjecture), which implies equivalent conjectures stated in A000668.
%t f[n_]:=Plus@@Divisors[Plus@@Divisors[n]-n]==n; lst={};Do[If[f[n],AppendTo[lst,n]],{n,9!}];lst (* _Vladimir Joseph Stephan Orlovsky_, May 14 2010 *)
%t Select[Range[550000],DivisorSigma[1,DivisorSigma[1,#]-#]==#&] (* The program generates the first 7 terms of the sequence. Increasing the Range constant will generate more but it will run a long time. *) (* _Harvey P. Dale_, May 08 2018 *)
%o (PARI) isok(n) = sigma(sigma(n)-n) == n; \\ _Michel Marcus_, May 06 2016
%Y Cf. A000043.
%K nonn,more
%O 1,1
%A _Benoit Cloitre_, Jul 27 2002
%E a(6) inserted by _Jaroslav Krizek_, Jun 29 2012