A123101 lambda(phi(n))=phi(lambda(n)) for the sequential application of Euler totient and Carmichael lambda functions.
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, 38, 42, 44, 46, 47, 51, 54, 56, 57, 59, 64, 65, 66, 68, 69, 72, 76, 81, 83, 84, 88, 92, 94, 102, 104, 105, 107, 108, 112, 114, 118, 128, 130, 132, 138, 140, 141, 144, 145, 152, 156
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n=1..1000
- W. D. Banks, F. Luca et al., Compositions with the Euler and Carmichael Functions, Ab Math Sem Univ Hamburg 75 (2005) 215-243.
Programs
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Mathematica
Cases[Range[100], k_ /; EulerPhi[CarmichaelLambda[k]] == CarmichaelLambda[EulerPhi[k]]] (* Artur Jasinski, Apr 05 2008 *)
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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,",") ); ); }