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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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6
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| 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.
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LINKS
| Eric Weisstein's World of Mathematics, Carmichael Function.
Eric Weisstein's World of Mathematics, Modulo Multiplication Group.
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FORMULA
| a(n) = A002322(2*n), n<>2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 28 2004
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MATHEMATICA
| Table[ If[ n==1, 1, LCM@@Map[ (#1[ [ 1 ] ]-1)*#1[ [ 1 ] ]^(#1[ [ 2 ] ]-1)&, FactorInteger[ n ] ] ], {n, 1, 70} ] (* Olivier Gerard, Aug 1997 *)
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PROG
| (PARI) a(n)=lcm( apply( f -> (f[1]-1)*f[1]^(f[2]-1), Vec(factor(n)~))) \\ - M. F. Hasler, Oct 23 2011
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CROSSREFS
| Cf. A002322.
Sequence in context: A004085 A086296 A096504 * A080737 A152455 A000010
Adjacent sequences: A011770 A011771 A011772 * A011774 A011775 A011776
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Thierry Moreau (Thierry.Moreau(AT)connotech.com), Simon Plouffe (simon.plouffe(AT)gmail.com).
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EXTENSIONS
| Description corrected by Antti Karttunen, Jan 09 2000
Definition made more explicit by M. F. Hasler, Oct 23 2011
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