Italy February Round 2025 P5

On 100 lines of a notebook, Federico writes 100 numbers calculated as follows: on the $n$-th line, he writes the number of prime numbers less than or equal to $n$ if $n$ is even, and the number of positive integers less than or equal to $n$ that are not prime if $n$ is odd. Finally, he adds together all 100 numbers he has written. What result does he obtain?

import Mathlib.NumberTheory.PrimeCounting

open Nat.Prime

def answer : ℤ := sorry

def f (n : ℕ) : ℤ := if Even n then π n else n - π n

theorem solution : ∑ i ∈ Finset.range 100, f i.succ = answer := sorry

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