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A129759 For the Landau function L(n), A000793, this sequence gives the largest prime which is a factor of L(n). 2


%S 1,2,3,2,3,3,3,5,5,5,5,5,5,7,7,7,7,7,7,7,7,7,7,7,7,7,11,11,7,11,11,13,

%T 13,11,11,11,11,13,13,11,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,

%U 13,17,17,17,17,17,19,19,17,17,17,17,19,19,17,17,19,19,19,19,19,19,17,19

%N For the Landau function L(n), A000793, this sequence gives the largest prime which is a factor of L(n).

%C This function is not monotone increasing, for example a(33) = 13 while a(34) = 11.

%C Nicolas showed that a(n) ~ sqrt(n log n) and Grantham showed that a(n) <= 1.328 sqrt(n log n) for n > 4. Massias, Nicolas, & Robin conjecture that a(n) <= 1.265... sqrt(n log n) in this range with equality at n = 215. - _Charles R Greathouse IV_, Jun 02 2014

%D J. L. Nicolas, Ordre maximal d'un élément du groupe des permutations et "highly composite numbers", Bull. Soc. Math. France 97 (1969), pp. 129-191.

%H Alois P. Heinz, <a href="/A129759/b129759.txt">Table of n, a(n) for n = 1..10000</a>

%H Jon Grantham, <a href="http://www.pseudoprime.com/maxord.html">The largest prime divisor of the maximal order of an element of S_n</a>, Math. Comp. 64:209 (1995), pp. 407-410.

%H J. P. Massias, J. L. Nicolas and G. Robin, <a href="http://math.univ-lyon1.fr/~nicolas/gdenMathComp.pdf">Effective bounds for the maximal order of an element in the symmetric group</a>, Math. Comp. 53:188 (1989), pp. 665-678. [<a href="http://www.ams.org/journals/mcom/1989-53-188/S0025-5718-1989-0979940-4/S0025-5718-1989-0979940-4.pdf">alternate link</a>]

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LandausFunction.html">Landau's Function</a>

%F a(n) = A006530(A000793(n)). - _R. J. Mathar_, May 17 2007

%e L(29) = 2520, whose largest prime factor is 7. So a(29) = 7.

%Y Cf. A000793, A128305.

%K nonn,look

%O 1,2

%A _Anthony C Robin_, May 15 2007

%E More terms from _Klaus Brockhaus_ and _R. J. Mathar_, May 16 2007

%E Corrected a(66) by _Alois P. Heinz_, Feb 16 2013

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Last modified February 16 19:29 EST 2019. Contains 320167 sequences. (Running on oeis4.)