

A129759


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


2



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, 13, 11, 11, 11, 11, 13, 13, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 19, 19, 17, 17, 17, 17, 19, 19, 17, 17, 19, 19, 19, 19, 19, 19, 17, 19
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OFFSET

1,2


COMMENTS

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


REFERENCES

J. L. Nicolas, Ordre maximal d'un élément du groupe des permutations et "highly composite numbers", Bull. Soc. Math. France 97 (1969), pp. 129191.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000
Jon Grantham, The largest prime divisor of the maximal order of an element of S_n, Math. Comp. 64:209 (1995), pp. 407410.
J. P. Massias, J. L. Nicolas and G. Robin, Effective bounds for the maximal order of an element in the symmetric group, Math. Comp. 53:188 (1989), pp. 665678. [alternate link]
Eric Weisstein's World of Mathematics, Landau's Function


FORMULA

a(n) = A006530(A000793(n)).  R. J. Mathar, May 17 2007


EXAMPLE

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


CROSSREFS

Cf. A000793, A128305.
Sequence in context: A102351 A078173 A248005 * A137467 A261461 A078627
Adjacent sequences: A129756 A129757 A129758 * A129760 A129761 A129762


KEYWORD

nonn,look


AUTHOR

Anthony C Robin, May 15 2007


EXTENSIONS

More terms from Klaus Brockhaus and R. J. Mathar, May 16 2007
Corrected a(66) by Alois P. Heinz, Feb 16 2013


STATUS

approved



