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A011773
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Variant of Carmichael's lambda function: a(p1^e1*...*pN^eN) = LCM((p1-1)*p1^(e1-1),...,(pN-1)*pN^(eN-1)).
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7
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1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 2, 12, 6, 4, 8, 16, 6, 18, 4, 6, 10, 22, 4, 20, 12, 18, 6, 28, 4, 30, 16, 10, 16, 12, 6, 36, 18, 12, 4, 40, 6, 42, 10, 12, 22, 46, 8, 42, 20, 16, 12, 52, 18, 20, 12, 18, 28, 58, 4, 60, 30, 6, 32, 12, 10, 66, 16, 22, 12
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OFFSET
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1,3
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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.
Eric Weisstein's World of Mathematics, Carmichael Function.
Eric Weisstein's World of Mathematics, Modulo Multiplication Group.
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FORMULA
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a(n) = A002322(2*n), for n != 2. - Vladeta Jovovic, Feb 28 2004
a(n) = LCM(A085730(A095874(A027748(n,k)^A124010(n,k))): k=1..A001221(n)). - Reinhard Zumkeller, Feb 16 2012
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MATHEMATICA
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Table[ If[ n==1, 1, LCM@@Map[ (#1[ [ 1 ] ]-1)*#1[ [ 1 ] ]^(#1[ [ 2 ] ]-1)&, FactorInteger[ n ] ] ], {n, 1, 70} ] (* Olivier Gérard, Aug 1997 *)
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PROG
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(PARI) a(n)=lcm( apply( f -> (f[1]-1)*f[1]^(f[2]-1), Vec(factor(n)~))) \\ M. F. Hasler, Oct 23 2011
(Haskell)
a011773 n = foldl lcm 1 $ map (a085730 . a095874) $
zipWith (^) (a027748_row n) (a124010_row n)
-- Reinhard Zumkeller, Feb 16 2012
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CROSSREFS
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Cf. A002322.
Sequence in context: A004085 A086296 A096504 * A080737 A152455 A000010
Adjacent sequences: A011770 A011771 A011772 * A011774 A011775 A011776
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Thierry Moreau (Thierry.Moreau(AT)connotech.com), Simon Plouffe
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EXTENSIONS
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Description corrected by Antti Karttunen, Jan 09 2000
Definition made more explicit by M. F. Hasler, Oct 23 2011
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STATUS
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approved
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