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%I #13 Aug 28 2020 06:17:55
%S 1,2,3,4,5,6,7,9,10,11,14,15,16,18,19,20,21,22,23,27,28,30,32,33,36,
%T 38,42,44,46,47,51,54,56,57,59,64,65,66,68,69,72,76,81,83,84,88,92,94,
%U 102,104,105,107,108,112,114,118,128,130,132,138,140,141,144,145,152,156
%N lambda(phi(n))=phi(lambda(n)) for the sequential application of Euler totient and Carmichael lambda functions.
%H T. D. Noe, <a href="/A123101/b123101.txt">Table of n, a(n) for n=1..1000</a>
%H W. D. Banks, F. Luca et al., Compositions with the Euler and Carmichael Functions, <a href="http://www.math.wfu.edu/publications/saidak/hamburg.pdf">Ab Math Sem Univ Hamburg 75 (2005) 215-243</a>.
%F A000010(A002322(n))=A002322(A000010(n)).
%t Cases[Range[100], k_ /; EulerPhi[CarmichaelLambda[k]] == CarmichaelLambda[EulerPhi[k]]] (* _Artur Jasinski_, Apr 05 2008 *)
%o (PARI) lambda(p,alpha)={ if(p>=3 || alpha<=2, return(p^(alpha-1)*(p-1)), return(2^(alpha-2)); ); } A002322(n)={ local(pf,rmax,resul); if(n==1, return(1) ); pf=factor(n); rmax=matsize(pf)[1]; resul= lambda(pf[1,1],pf[1,2]); for(r=2,rmax, resul=lcm(resul,lambda(pf[r,1],pf[r,2])); ); return(resul); } { for(n=1,300, if( eulerphi(A002322(n))==A002322(eulerphi(n)), print1(n,",") ); ); }
%Y Cf. A002332, A000010.
%K easy,nonn
%O 1,2
%A _R. J. Mathar_, Sep 27 2006
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