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

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..10.

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A000043.

Sequence in context: A227295 A034785 A247938 * A075398 A358408 A098579

Adjacent sequences: A072865 A072866 A072867 * A072869 A072870 A072871

Keyword

nonn,more

Author

Benoit Cloitre, Jul 27 2002

Extensions

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

Status

approved