`arith_landau_function_vec`

Synopsis#include <flint/arith.h>

void arith_landau_function_vec(fmpz * res, slong len)source

Sets res to the first len values $g(0), g(1), \ldots$ of Landau's function, the largest order of an element of the symmetric group $S_n$ , equivalently the largest $\operatorname{lcm}(n_1, \ldots, n_r)$ with $n_1 + \cdots + n_r \le n$ .

Implements the basic algorithm of [DelegliseNicolasZimmermann2009], a dynamic programme over the prime powers $p^e \le n$ for primes $p$ up to about $1.33\sqrt{n \log n}$ . The running time is $O(n^{3/2} / \sqrt{\log n})$ operations on integers of $O(\sqrt{n \log n})$ bits.

References#

[DelegliseNicolasZimmermann2009] Deleglise, Marc and Niclas, Jean-Louis and Zimmermann, Paul : Landau's function for one million billions, J. Théor. Nombres Bordeaux 20:3 (2009) 625–671

Cite this page

The FLINT team, “arith_landau_function_vec (arith.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arith/arith_landau_function_vec.html (generated 2026-11-02).

@misc{flint-doc-arith-arith-landau-function-vec,
  author       = {{The FLINT team}},
  title        = {{arith\_landau\_function\_vec (arith.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/arith/arith_landau_function_vec.html},
  note         = {Generated 2026-11-02}
}

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