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%I #46 Sep 19 2020 16:14:08
%S 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,
%T 4,30,16,10,16,12,6,36,18,12,4,40,6,42,10,12,22,46,8,42,20,16,12,52,
%U 18,20,12,18,28,58,4,60,30,6,32,12,10,66,16,22,12
%N Variant of Carmichael's lambda function: a(p1^e1*...*pN^eN) = lcm((p1-1)*p1^(e1-1), ..., (pN-1)*pN^(eN-1)).
%H Reinhard Zumkeller, <a href="/A011773/b011773.txt">Table of n, a(n) for n = 1..10000</a>
%H L. Blum; M. Blum; M. Shub, <a href="http://dx.doi.org/10.1137/0215025">A simple unpredictable pseudorandom number generator</a>, SIAM J. Comput. 15 (1986), no. 2, 364-383. see p. 377.
%H J.-H. Evertse and E. van Heyst, <a href="http://dx.doi.org/10.1007/3-540-46877-3_8">Which new RSA signatures can be computed from some given RSA signatures?</a>, Proceedings of Eurocrypt'90, Lect. Notes Comput. Sci., 473, Springer-Verlag, pp. 84-97, see page 86.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CarmichaelFunction.html">Carmichael Function.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ModuloMultiplicationGroup.html">Modulo Multiplication Group.</a>
%F a(n) = A002322(2*n), for n != 2. - _Vladeta Jovovic_, Feb 28 2004
%F a(n) = lcm_{k=1..A001221(n)} A085730(A095874(A027748(n,k)^A124010(n,k))). - _Reinhard Zumkeller_, Feb 16 2012
%t Table[ If[ n==1, 1, LCM@@Map[ (#1[ [ 1 ] ]-1)*#1[ [ 1 ] ]^(#1[ [ 2 ] ]-1)&, FactorInteger[ n ] ] ], {n, 1, 70} ] (* _Olivier Gérard_, Aug 1997 *)
%t a[2] = 1;
%t a[n_] := CarmichaelLambda[2n];
%t Array[a, 1000] (* _Jean-François Alcover_, Sep 19 2020 *)
%o (PARI) a(n)=lcm( apply( f -> (f[1]-1)*f[1]^(f[2]-1), Vec(factor(n)~))) \\ _M. F. Hasler_, Oct 23 2011
%o (Haskell)
%o a011773 n = foldl lcm 1 $ map (a085730 . a095874) $
%o zipWith (^) (a027748_row n) (a124010_row n)
%o -- _Reinhard Zumkeller_, Feb 16 2012
%Y Cf. A002322.
%K nonn,nice,easy
%O 1,3
%A Thierry Moreau (Thierry.Moreau(AT)connotech.com), _Simon Plouffe_
%E Description corrected by _Antti Karttunen_, Jan 09 2000
%E Definition made more explicit by _M. F. Hasler_, Oct 23 2011
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