%I A002322 M0298 N0110
%S A002322 1,1,2,2,4,2,6,2,6,4,10,2,12,6,4,4,16,6,18,4,6,10,22,2,20,12,18,6,28,4,
%T A002322 30,8,10,16,12,6,36,18,12,4,40,6,42,10,12,22,46,4,42,20,16,12,52,18,20,
               6,
%U A002322 18,28,58,4,60,30,6,16,12,10,66,16,22,12,70,6,72,36,20,18,30,12,78,4,54
%N A002322 Reduced totient function psi(n): least k such that x^k == 1 (mod n) for 
               all x prime to n; also Carmichael lambda function (exponent of unit 
               group mod n).
%C A002322 Largest period of repeating digits of 1/n written in different bases 
               (i.e. largest value in each row of square array A066799 and least 
               common multiple of each row). - Henry Bottomley (se16(AT)btinternet.com), 
               Dec 20 2001
%D A002322 L. Blum; M. Blum; M. Shub, A simple unpredictable pseudorandom number 
               generator. SIAM J. Comput. 15 (1986), no. 2, 364-383. see p. 377.
%D A002322 J.-H. Evertse and E. van Heyst, Which new RSA signatures can be computed 
               from some given RSA signatures?, Proceedings of Eurocrypt'90, Lect. 
               Notes Comput. Sci., 473, Springer-Verlag, pp. 84-97, see page 86.
%D A002322 D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 
               105, National Research Council, Washington, DC, 1941, pp. 7-10.
%D A002322 Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 
               1984, page 269.
%D A002322 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002322 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002322 T. D. Noe, <a href="b002322.txt">Table of n, a(n) for n = 1..10000</a>
%H A002322 A. Cauchy, Memoire sur la resolution des equations indeterminees du premier 
               degre en nombres entiers, <a href="http://gallica.bnf.fr/scripts/
               ConsultationTout.exe?E=0&O=N090204">Oeuvres Compl\`{e}tes</a>. Gauthier-Villars, 
               Paris, 1882-1938, Series (2), Vol. 12, pp. 9-47.
%H A002322 A. de Vries, <a href="http://math-it.org/Mathematik/Zahlentheorie/Zahl/
               ZahlApplet.html">The prime factors of an integer(along with Euler's 
               phi and Carmichael's lambda functions)</a>
%H A002322 P. Pollack, <a href="http://www.math.dartmouth.edu/~ppollack/notes.pdf">
               Analytic and Combinatorial Number Theory</a> Course Notes, p. 80.
%H A002322 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CarmichaelFunction.html">Link to a section of The World of Mathematics.</
               a>
%H A002322 Wolfram Research, <a href="http://functions.wolfram.com/NumberTheoryFunctions/
               CarmichaelLambda/03/02">First 50 vaues of Carmichael lambda(n)</a>
%H A002322 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%F A002322 If M=2^e*P1^e1*P2^e2*...*Pk^ek, lambda(2^e) =2^(e-1) if e=1 or 2, =2^(e-2) 
               if e>2; lambda(M)=LCM{ lambda(2^e), (P1-1)*P1^(e1-1), (P2-1)*P2^(e2-1), 
               ..., (Pk-1)*Pk^(ek-1)}.
%F A002322 Any number of the sequence in position "p", "p" a prime, is equal to 
               p-1. - Paolo P. Lava (ppl(AT)spl.at), Oct 02 2006
%p A002322 with(numtheory); A002322 := lambda; [seq(lambda(n), n=1..)];
%t A002322 Table[CarmichaelLambda[k], {k, 50}] - Artur Jasinski (grafix(AT)csl.pl), 
               Apr 05 2008
%o A002322 (MAGMA) [1] cat [ CarmichaelLambda(n) : n in [2..100]];
%o A002322 (PARI) A002322(n)= lcm( apply( f -> (f[1]-1)*f[1]^(f[2]-1-(f[1]==2 && 
               f[2]>2)), Vec(factor(n)~))) \\ [From M. F. Hasler (MHasler(AT)univ-ag.fr), 
               Jul 05 2009]
%Y A002322 Cf. A011773, A002174, A002616, A034380, A061258, A062373.
%Y A002322 Cf. A002616.
%Y A002322 Sequence in context: A122457 A139770 A140635 this_sequence A127835 A117004 
               A128982
%Y A002322 Adjacent sequences: A002319 A002320 A002321 this_sequence A002323 A002324 
               A002325
%K A002322 nonn,core,easy,nice
%O A002322 1,3
%A A002322 N. J. A. Sloane (njas(AT)research.att.com).