MathDB

In a blackboard there are

K

circles in a row such that one of the numbers

1,...,K

is assigned to each circle from the left to the right. Change of situation of a circle is to write in it or erase the number which is assigned to it.At the beginning no number is written in its own circle. For every positive divisor

d

K

1\leq d\leq K

we change the situation of the circles in which their assigned numbers are divisible by

d

,performing for each divisor

d

K

changes of situation. Determine the value of

K

for which the following holds;when this procedure is applied once for all positive divisors of

K

,then all numbers

1,2,3,...,K

are written in the circles they were assigned in.

Problem Statement