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CNCM Online Round 3
3
3
Part of
CNCM Online Round 3
Problems
(1)
CNCM Online R3 P3
Source:
11/7/2020
Let
a
1
=
1
a_1 = 1
a
1
=
1
and
a
n
+
1
=
a
n
⋅
p
n
a_{n+1} = a_n \cdot p_n
a
n
+
1
=
a
n
⋅
p
n
for
n
≥
1
n \geq 1
n
≥
1
where
p
n
p_n
p
n
is the
n
n
n
th prime number, starting with
p
1
=
2
p_1 = 2
p
1
=
2
. Let
τ
(
x
)
\tau(x)
τ
(
x
)
be equal to the number of divisors of
x
x
x
. Find the remainder when
∑
n
=
1
2020
∑
d
∣
a
n
τ
(
d
)
\sum_{n=1}^{2020} \sum_{d \mid a_n} \tau (d)
n
=
1
∑
2020
d
∣
a
n
∑
τ
(
d
)
is divided by 91 for positive integers
d
d
d
. Recall that
d
∣
a
n
d|a_n
d
∣
a
n
denotes that
d
d
d
divides
a
n
a_n
a
n
. Proposed by Minseok Eli Park (wolfpack)
CNCM