SELECT 
  category_id, 
  parent_id 
FROM 
  cscart_categories 
WHERE 
  parent_id IN(
    18416, 18531, 18532, 18533, 18536, 18545, 
    18546, 18552, 18558, 18584, 18596, 
    18620, 18621, 18641, 18646, 18647, 
    18648, 18649
  ) 
  AND category_id != 1

Query time 0.00008

JSON explain

{
  "query_block": {
    "select_id": 1,
    "nested_loop": [
      {
        "table": {
          "table_name": "cscart_categories",
          "access_type": "range",
          "possible_keys": ["PRIMARY", "parent", "p_category_id"],
          "key": "parent",
          "key_length": "3",
          "used_key_parts": ["parent_id"],
          "rows": 93,
          "filtered": 100,
          "index_condition": "cscart_categories.parent_id in (18416,18531,18532,18533,18536,18545,18546,18552,18558,18584,18596,18620,18621,18641,18646,18647,18648,18649)",
          "attached_condition": "cscart_categories.category_id <> 1"
        }
      }
    ]
  }
}