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Kvant 2020
M2607
M2607
Part of
Kvant 2020
Problems
(1)
Set with a divisibility criterion
Source: Kvant Magazine No. 6 2020 M2607
3/9/2023
Let
n
n
n
be a natural number. The set
A
A{}
A
of natural numbers has the following property: for any natural number
m
⩽
n
m\leqslant n
m
⩽
n
in the set
A
A{}
A
there is a number divisible by
m
m{}
m
. What is the smallest value that the sum of all the elements of the set
A
A{}
A
can take?Proposed by A. Kuznetsov
number theory
Kvant