

A011773


Variant of Carmichael's lambda function: a(p1^e1*...*pN^eN) = lcm((p11)*p1^(e11), ..., (pN1)*pN^(eN1)).


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
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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, 364383. 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, SpringerVerlag, pp. 8497, 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] (* JeanFrançois 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



