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%I #13 Sep 25 2017 06:00:32
%S 2,4,16,25,64,4096,65536,262144,1073741824
%N Numbers n such that f(f(f(n))) = f(f(n)) + f(n) where f = A000203.
%C Numbers n such that A066971(n) = A051027(n) + A000203(n).
%C A061652 is a subsequence.
%C Are there any odd terms other than 25?
%e 25 = 5^2 is a term because sigma(sigma(sigma(5^2))) = sigma(2^5) = sigma(sigma(5^2)) + sigma(5^2).
%t 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 *)
%o (PARI) s(n) = sigma(n);
%o isok(n) = s(s(s(n)))==s(s(n))+s(n);
%Y Cf. A000203, A019279, A051027, A061652, A066971.
%K nonn,more
%O 1,1
%A _Altug Alkan_, Sep 15 2017
%E a(9) from _Giovanni Resta_, Sep 15 2017
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