HAPPY 2019!

Do you know......?

• The number 2019, its double 4038, and its triple 6057 contain all 10 digits. What is the next number with this property?
• The number 2019 can be written as the sum of the first n perfect powers (integers of the form a^m where a>0 and m≥2). What is the value of n?
• 2019 is the smallest number that can be written as the sum of the squares of 3 primes, p²+q²+r², in n different ways (where the order doesn't matter). What is the value of n?