FLINT3.7.0-dev
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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 2026-10-20).