p1. Consider the sequence of positive integers $2, 3, 5, 6, 7, 8, 10, 11 ...$. which are not perfect squares. Calculate the $2019$-th term of the sequence.


p2. In a triangle $ABC$, let $D$ be the midpoint of side $BC$ and $E$ be the midpoint of segment $AD$. Lines $AC$ and $BE$ intersect at $F$. Show that $3AF = AC$.


p3. Find all positive integers $n$ such that $n! + 2019$ is a square perfect. 


p4. In a party,  there is a certain group of people, none of whom has more than $3$ friends in this. However, if two people are not friends at least they have a friend in this party.  What is the largest possible number of people in the party?
To find the 2019-th term of the sequence of positive integers that are not perfect squares, we need to follow these steps:

1. **Identify the number of perfect squares less than 2019:**
   We need to find the largest integer \( n \) such that \( n^2 < 2019 \).
   \[
   44^2 = 1936 < 2019 < 2025 = 45^2
   \]
   Therefore, there are 44 perfect squares less than 2019.

2. **Determine the position in the sequence:**
   The sequence of all positive integers up to 2019 is:
   \[
   1, 2, 3, \ldots, 2019
   \]
   Removing the 44 perfect squares from this sequence, we get:
   \[
   2, 3, 5, 6, 7, 8, 10, 11, \ldots, 2019
   \]
   This sequence has \( 2019 - 44 = 1975 \) elements.

3. **Extend the sequence to find the 2019-th term:**
   Since we need the 2019-th term, we need to add more terms beyond 2019. We need \( 2019 - 1975 = 44 \) more terms. We continue the sequence beyond 2019, skipping perfect squares:
   \[
   2020, 2021, 2022, 2023, 2024, 2026, 2027, \ldots
   \]
   Notice that 2025 is a perfect square and should be skipped.

4. **Calculate the 2019-th term:**
   We need to add 44 more terms to the sequence of 1975 terms. The next 44 terms after 2019, skipping perfect squares, are:
   \[
   2020, 2021, 2022, 2023, 2024, 2026, 2027, \ldots, 2063, 2064
   \]
   Therefore, the 2019-th term of the sequence is 2064.

The final answer is \(\boxed{2064}\)