Fungrim home page

Fungrim entry: 7932c3

g(n)=max{lcm ⁣(s1,,sk):kZ0  and  siZ1  and  i=1ksi=n}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:nZ1n \in \mathbb{Z}_{\ge 1}
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}
Fungrim symbol Notation Short description
LandauGg(n)g(n) Landau's function
MaximummaxxSf(x)\mathop{\max}\limits_{x \in S} f(x) Maximum value of a set or function
LCMlcm ⁣(a,b)\operatorname{lcm}\!\left(a, b\right) Least common multiple
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Sumnf(n)\sum_{n} f(n) Sum
Source code for this entry:
    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)))))),
    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