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Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2014 Switzerland - Final Round
9
9
Part of
2014 Switzerland - Final Round
Problems
(1)
a_n=0 or according to parity of number of divisors > 2014
Source: Switzerland - 2014 Swiss MO Final Round p9
1/14/2023
The sequence of integers
a
1
,
a
2
,
,
,
a_1, a_2, ,,
a
1
,
a
2
,,,
is defined as follows:
a
n
=
{
0
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n
h
a
s
a
n
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v
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n
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m
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s
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e
a
t
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t
h
a
n
2014
1
i
f
n
h
a
s
a
n
o
d
d
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a
n
2014
a_n=\begin{cases} 0\,\,\,\, if\,\,\,\, n\,\,\,\, has\,\,\,\, an\,\,\,\, even\,\,\,\, number\,\,\,\, of\,\,\,\, divisors\,\,\,\, greater\,\,\,\, than\,\,\,\, 2014 \\ 1 \,\,\,\, if \,\,\,\, n \,\,\,\, has \,\,\,\, an \,\,\,\, odd \,\,\,\, number \,\,\,\, of \,\,\,\, divisors \,\,\,\, greater \,\,\,\, than \,\,\,\, 2014\end{cases}
a
n
=
{
0
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f
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d
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sors
g
re
a
t
er
t
han
2014
1
i
f
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sors
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re
a
t
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t
han
2014
Show that the sequence
a
n
a_n
a
n
never becomes periodic.
number theory
periodic
Divisors