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Turkey Team Selection Test
2024 Turkey Team Selection Test
8
8
Part of
2024 Turkey Team Selection Test
Problems
(1)
A sequence related to the sigma function
Source: 2024 Turkey TST P8
3/18/2024
For an integer
n
n
n
,
σ
(
n
)
\sigma(n)
σ
(
n
)
denotes the sum of postitive divisors of
n
n
n
. A sequence of positive integers
(
a
i
)
i
=
0
∞
(a_i)_{i=0}^{\infty}
(
a
i
)
i
=
0
∞
with
a
0
=
1
a_0 =1
a
0
=
1
is defined as follows: For each
n
>
1
n>1
n
>
1
,
a
n
a_n
a
n
is the smallest integer greater than
1
1
1
that satisfies
σ
(
a
0
a
1
…
a
n
−
1
)
∣
σ
(
a
0
a
1
…
a
n
)
.
\sigma{(a_0a_1\dots a_{n-1})} \vert \sigma{(a_0a_1\dots a_{n})}.
σ
(
a
0
a
1
…
a
n
−
1
)
∣
σ
(
a
0
a
1
…
a
n
)
.
Determine the number of divisors of
202
4
2024
2024^{2024}
202
4
2024
amongst the sequence.
number theory