# Fungrim entry: 7932c3

$g\!\left(n\right) = \max \left\{ \operatorname{lcm}\!\left({s}_{1}, \ldots, {s}_{k}\right) : k \in \mathbb{Z}_{\ge 0} \,\mathbin{\operatorname{and}}\, {s}_{i} \in \mathbb{Z}_{\ge 1} \,\mathbin{\operatorname{and}}\, \sum_{i=1}^{k} {s}_{i} = n \right\}$
Assumptions:$n \in \mathbb{Z}_{\ge 1}$
TeX:
g\!\left(n\right) = \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$g\!\left(n\right)$ Landau's function
Maximum$\mathop{\max}\limits_{P\left(x\right)} f\!\left(x\right)$ Maximum value of a set or function
SetBuilder$\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension
LCM$\operatorname{lcm}\!\left(a, b\right)$ Least common multiple
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Sum$\sum_{n} f\!\left(n\right)$ Sum
Source code for this entry:
Entry(ID("7932c3"),
Formula(Equal(LandauG(n), Maximum(SetBuilder(LCM(Subscript(s, 1), Ellipsis, Subscript(s, k)), Tuple(k, Subscript(s, i)), And(Element(k, ZZGreaterEqual(0)), Element(Subscript(s, i), ZZGreaterEqual(1)), Equal(Sum(Subscript(s, i), Tuple(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.

2019-08-21 11:44:15.926409 UTC