A072868 Numbers k such that sigma(sigma(k) - k) = k.

4, 8, 32, 128, 8192, 131072, 524288, 2147483648, 2305843009213693952, 618970019642690137449562112

Offset: 1

Author

Benoit Cloitre, Jul 27 2002

Keywords

• nonn
• more

Comments

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

Crossrefs

Cf. A000043.

Programs

Mathematica

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 *)
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 *)

PARI

isok(n) = sigma(sigma(n)-n) == n; \\ Michel Marcus, May 06 2016

Formula

a(n) = 1 + A000668(n) (conjecture), which implies equivalent conjectures stated in A000668.

Extensions

a(6) inserted by Jaroslav Krizek, Jun 29 2012