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

1,2

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.

Formula

A000010(A002322(n))=A002322(A000010(n)).

Mathematica

Cases[Range[100], k_ /; EulerPhi[CarmichaelLambda[k]] == CarmichaelLambda[EulerPhi[k]]] (* Artur Jasinski, Apr 05 2008 *)

Prog

(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, ", ") ); ); }

Crossrefs

Cf. A002332, A000010.

Sequence in context: A193838 A174328 A272570 * A071557 A331802 A271108

Adjacent sequences: A123098 A123099 A123100 * A123102 A123103 A123104

Keyword

easy,nonn

Author

R. J. Mathar, Sep 27 2006

Status

approved