A292369 Numbers n such that f(f(f(n))) = f(f(n)) + f(n) where f = A000203.

2, 4, 16, 25, 64, 4096, 65536, 262144, 1073741824

Offset

1,1

Comments

Numbers n such that A066971(n) = A051027(n) + A000203(n).

A061652 is a subsequence.

Are there any odd terms other than 25?

Links

Table of n, a(n) for n=1..9.

Example

25 = 5^2 is a term because sigma(sigma(sigma(5^2))) = sigma(2^5) = sigma(sigma(5^2)) + sigma(5^2).

Mathematica

f[n_] := DivisorSigma[1, n]; fQ[n_] := f[f[f[n]]] == f[f[n]] + f[n]; Select[ Range@1000000, fQ] (* Robert G. Wilson v, Sep 23 2017 *)

Prog

(PARI) s(n) = sigma(n);
isok(n) = s(s(s(n)))==s(s(n))+s(n);

Crossrefs

Cf. A000203, A019279, A051027, A061652, A066971.

Sequence in context: A275674 A225983 A298080 * A357917 A153665 A015775

Adjacent sequences: A292366 A292367 A292368 * A292370 A292371 A292372

Keyword

nonn,more

Author

Altug Alkan, Sep 15 2017

Extensions

a(9) from Giovanni Resta, Sep 15 2017

Status

approved