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A123101 lambda(phi(n))=phi(lambda(n)) for the sequential application of Euler totient and Carmichael lambda functions. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A117730 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

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Last modified April 23 04:23 EDT 2021. Contains 343199 sequences. (Running on oeis4.)