To estimate a maximum purchase price for the coin that will be auctioned, we can consider several factors based on the provided data:

1. Starting Price: The starting price is 110 euros, which indicates the starting point for the auction.

2. Auction History: The coin has been auctioned 18 times in the past, of which it has sold 13 times. This suggests there is considerable interest in the coin.

3. Previous Hammer Prices: Previous hammer prices have varied, but there are several examples where the hammer price has reached or exceeded 110 euros. For example:
- In 2020, it was hammered at 110 euros.
- In 2018, it was hammered at 110 euros.
- In 2014, it was hammered at 155 euros.

4. Average Hammer Price: The average hammer price is 126 euros, indicating that, on average, similar coins have reached a price above the starting price.

5. Condition: There is no information about the condition of this coin, which may affect its value. However, since there have been successful sales in the past, we can assume that the coin has a reasonable value.

6. Price Trends: Hammer prices have shown a trend of being above the starting price, suggesting that bidders are willing to pay more.

Based on these factors, an estimated maximum purchase price could be in the range of 130 to 150 euros. This is based on the average hammer price and previous hammer prices that have exceeded the starting price.

Therefore, a reasonable estimated maximum purchase price could be 150 euros.