# Fungrim entry: 7932c3

$g(n) = \max \left\{ \operatorname{lcm}\!\left({s}_{1}, \ldots, {s}_{k}\right) : k \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; {s}_{i} \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \sum_{i=1}^{k} {s}_{i} = n \right\}$
Assumptions:$n \in \mathbb{Z}_{\ge 1}$
TeX:
g(n) = \max \left\{ \operatorname{lcm}\!\left({s}_{1}, \ldots, {s}_{k}\right) : k \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; {s}_{i} \in \mathbb{Z}_{\ge 1} \;\mathbin{\operatorname{and}}\; \sum_{i=1}^{k} {s}_{i} = n \right\}

n \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
LandauG$g(n)$ Landau's function
Maximum$\mathop{\max}\limits_{x \in S} f(x)$ Maximum value of a set or function
LCM$\operatorname{lcm}\!\left(a, b\right)$ Least common multiple
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Sum$\sum_{n} f(n)$ Sum
Source code for this entry:
Entry(ID("7932c3"),
Formula(Equal(LandauG(n), Maximum(Set(LCM(Subscript(s, 1), Ellipsis, Subscript(s, k)), For(Tuple(k, Subscript(s, i))), And(Element(k, ZZGreaterEqual(0)), Element(Subscript(s, i), ZZGreaterEqual(1)), Equal(Sum(Subscript(s, i), For(i, 1, k)), n)))))),
Variables(n),
Assumptions(Element(n, ZZGreaterEqual(1))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC