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2023 MOAA
16
2023 MOAA Gunga P16
2023 MOAA Gunga P16
Source:
October 15, 2023
MOAA 2023
Problem Statement
Compute the sum
φ
(
50
!
)
φ
(
49
!
)
+
φ
(
51
!
)
φ
(
50
!
)
+
⋯
+
φ
(
100
!
)
φ
(
99
!
)
\frac{\varphi(50!)}{\varphi(49!)}+ \frac{\varphi(51!)}{\varphi(50!)} + \dots + \frac{\varphi(100!)}{\varphi(99!)}
φ
(
49
!)
φ
(
50
!)
+
φ
(
50
!)
φ
(
51
!)
+
⋯
+
φ
(
99
!)
φ
(
100
!)
where
φ
(
n
)
\varphi(n)
φ
(
n
)
returns the number of positive integers less than
n
n
n
that are relatively prime to
n
n
n
.Proposed by Andy Xu
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