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Search: id:A002322
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| A002322 |
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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).
(Formerly M0298 N0110)
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+0
36
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| 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, 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, 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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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
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REFERENCES
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L. Blum; M. Blum; M. Shub, A simple unpredictable pseudorandom number generator. SIAM J. Comput. 15 (1986), no. 2, 364-383. see p. 377.
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. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, pp. 7-10.
Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 1984, page 269.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
A. Cauchy, Memoire sur la resolution des equations indeterminees du premier degre en nombres entiers, Oeuvres Compl\`{e}tes. Gauthier-Villars, Paris, 1882-1938, Series (2), Vol. 12, pp. 9-47.
A. de Vries, The prime factors of an integer(along with Euler's phi and Carmichael's lambda functions)
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 80.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Wolfram Research, First 50 vaues of Carmichael lambda(n)
Index entries for "core" sequences
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FORMULA
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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)}.
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
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MAPLE
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with(numtheory); A002322 := lambda; [seq(lambda(n), n=1..)];
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MATHEMATICA
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Table[CarmichaelLambda[k], {k, 50}] - Artur Jasinski (grafix(AT)csl.pl), Apr 05 2008
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PROGRAM
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(MAGMA) [1] cat [ CarmichaelLambda(n) : n in [2..100]];
(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]
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CROSSREFS
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Cf. A011773, A002174, A002616, A034380, A061258, A062373.
Cf. A002616.
Sequence in context: A122457 A139770 A140635 this_sequence A127835 A117004 A128982
Adjacent sequences: A002319 A002320 A002321 this_sequence A002323 A002324 A002325
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KEYWORD
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nonn,core,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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