

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


LINKS



FORMULA



EXAMPLE

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


MATHEMATICA

b[n_, i_] := b[n, i] = Module[{p}, p = If[i < 1, 1, Prime[i]]; If[n == 0  i < 1, 1, Max[b[n, i  1], Table[p^j*b[n  p^j, i  1], {j, 1, Log[p, n] // Floor}]]]];
g[n_] := b[n, If[n<8, 3, PrimePi[Ceiling[1.328*Sqrt[n*Log[n] // Floor]]]]];
a[n_] := FactorInteger[g[n]][[1, 1]];


CROSSREFS



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AUTHOR



EXTENSIONS



STATUS

approved



