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A011773 Variant of Carmichael's lambda function: a(p1^e1*...*pN^eN) = lcm((p1-1)*p1^(e1-1), ..., (pN-1)*pN^(eN-1)). 7
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; text; internal format)
OFFSET
1,3
LINKS
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.
FORMULA
a(n) = A002322(2*n), for n != 2. - Vladeta Jovovic, Feb 28 2004
a(n) = lcm_{k=1..A001221(n)} A085730(A095874(A027748(n,k)^A124010(n,k))). - Reinhard Zumkeller, Feb 16 2012
MATHEMATICA
Table[ If[ n==1, 1, LCM@@Map[ (#1[ [ 1 ] ]-1)*#1[ [ 1 ] ]^(#1[ [ 2 ] ]-1)&, FactorInteger[ n ] ] ], {n, 1, 70} ] (* Olivier Gérard, Aug 1997 *)
a[2] = 1;
a[n_] := CarmichaelLambda[2n];
Array[a, 1000] (* Jean-François Alcover, Sep 19 2020 *)
PROG
(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
CROSSREFS
Cf. A002322.
Sequence in context: A277906 A290077 A277030 * A306275 A322321 A080737
KEYWORD
nonn,nice,easy
AUTHOR
Thierry Moreau (Thierry.Moreau(AT)connotech.com), Simon Plouffe
EXTENSIONS
Description corrected by Antti Karttunen, Jan 09 2000
Definition made more explicit by M. F. Hasler, Oct 23 2011
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)