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%I #23 Sep 15 2017 03:14:22
%S 2,38040,51888,236644,260880,3097024,5283852,5667312,11777472,
%T 46120848,52981252,69128640,121352208,330364848,485906400,662736600,
%U 769422720,1111869360,1267978320,1272335760,1426817904,1807128528,2107406448,2381691312,2452404544,2691587568
%N 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.
%C 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?
%C Non-abundant terms are 2, 236644, 52981252,...
%C If an odd term exists, it is larger than 2*10^11. - _Giovanni Resta_, Sep 15 2017
%e 38040 is a term because sigma(38040) = 114480 and sigma(114480) = sigma(76440) + 114480.
%t inQ[n_] := DivisorSigma[1, DivisorSigma[1, n]] == DivisorSigma[1, DivisorSigma[1, n] - n] + DivisorSigma[1, n]; (* _Robert G. Wilson v_, Sep 10 2017 *)
%o (PARI) a001065(n) = sigma(n)-n;
%o isok(n) = sigma(a001065(n))==a001065(sigma(n));
%Y Cf. A000203, A001065, A051027, A072869.
%K nonn
%O 1,1
%A _Altug Alkan_, Sep 05 2017
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