1365

This number is a composite.

The smallest number that has four distinct prime factors whose arithmetic mean is also a prime number: 1365 = 3*5*7*13 and (3+5+7+13)/4 = 7. [Roldan]

1365 is the product of the first 4 odd Mersenne prime exponents (3, 5, 7, 13), which are also the first 4 Fortunate primes. Interestingly, it also equals σ₂(2⁵), the sum of the squares of the divisors of 2⁵, which expands to the geometric series 4⁰ + 4¹ + 4² + 4³ + 4⁴ + 4⁵. [Ahmed]