A291881 Numbers n such that sigma(sigma(n)) = sigma(sigma(n)-n) + sigma(n); that is, f(g(n)) = g(f(n)) where f = A000203 and g = A001065.

2, 38040, 51888, 236644, 260880, 3097024, 5283852, 5667312, 11777472, 46120848, 52981252, 69128640, 121352208, 330364848, 485906400, 662736600, 769422720, 1111869360, 1267978320, 1272335760, 1426817904, 1807128528, 2107406448, 2381691312, 2452404544, 2691587568

Offset: 1

Author

Altug Alkan, Sep 05 2017

Keywords

• nonn

Comments

Initial motivation for this sequence was that question: Can be an odd number k such that f(g(k)) = g(f(k)) where f = A000203 and g = A001065?

Non-abundant terms are 2, 236644, 52981252,...

If an odd term exists, it is larger than 2*10^11. - Giovanni Resta, Sep 15 2017

Examples

			38040 is a term because sigma(38040) = 114480 and sigma(114480) = sigma(76440) + 114480.
		

Crossrefs

Cf. A000203, A001065, A051027, A072869.

Programs

Mathematica

inQ[n_] :=  DivisorSigma[1, DivisorSigma[1, n]] == DivisorSigma[1, DivisorSigma[1, n] - n] + DivisorSigma[1, n]; (* Robert G. Wilson v, Sep 10 2017 *)

PARI

a001065(n) = sigma(n)-n;
isok(n) = sigma(a001065(n))==a001065(sigma(n));