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A096866 Function A062402(x) = sigma(phi(x)) is iterated. Starting with n, a(n) is the smallest term arising in trajectory, either in transient or in terminal cycle.

%I A096866 #13 Nov 18 2017 21:00:26
%S A096866 1,1,3,3,5,3,7,7,7,7,7,7,13,7,15,15,17,7,19,15,21,7,23,15,25,26,27,28,
%T A096866 29,15,31,31,28,31,31,28,37,31,31,31,31,28,43,28,31,28,31,31,49,28,51,
%U A096866 31,53,31,31,31,57,31,31,31,61,31,63,63,65,28,67,63,31,31,71,31,73,74
%N A096866 Function A062402(x) = sigma(phi(x)) is iterated. Starting with n, a(n) is the smallest term arising in trajectory, either in transient or in terminal cycle.
%H A096866 Antti Karttunen, <a href="/A096866/b096866.txt">Table of n, a(n) for n = 1..16384</a>
%e A096866 n=240: list={240,127,312,[252,195],252,...}, a(240)=127, a transient;
%e A096866 n=254: list={254,312,[252,195],252,...}, a(254)=195, a recurrent term.
%t A096866 gf[x_] :=DivisorSigma[1, EulerPhi[x]] gite[x_, hos_] :=NestList[gf, x, hos] Table[Min[gite[w, 20]], {w, 1, 256}]
%o A096866 (Scheme) (define (A096866 n) (let loop ((visited (list n)) (m n)) (let ((next (A062402 (car visited)))) (cond ((member next visited) m) (else (loop (cons next visited) (min m next))))))) ;; _Antti Karttunen_, Nov 18 2017
%Y A096866 Cf. A062401, A062402, A096862, A096863, A096864 (largest term), A096993.
%Y A096866 Cf. also A096865.
%K A096866 nonn
%O A096866 1,3
%A A096866 _Labos Elemer_, Jul 21 2004