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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
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 (list; graph; refs; listen; history; text; internal format)
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. 129-191.

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. 407-410.

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. 665-678. [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

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Last modified November 18 15:41 EST 2018. Contains 317323 sequences. (Running on oeis4.)