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Fungrim entry: 7932c3

g(n)=max{lcm ⁣(s1,,sk):kZ0andsiZ1andi=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}
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
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:
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))))

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

2019-10-05 13:11:19.856591 UTC