A011773 Variant of Carmichael's lambda function: a(p1^e1*...*pN^eN) = lcm((p1-1)*p1^(e1-1), ..., (pN-1)*pN^(eN-1)).

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

Offset

1,3

Links

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.

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

Adjacent sequences: A011770 A011771 A011772 * A011774 A011775 A011776

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