393129 has 27 divisors (see below), whose sum is σ = 658749. Its totient is φ = 225720.

The previous prime is 393121. The next prime is 393137. The reversal of 393129 is 921393.

The square root of 393129 is 627.

It is a perfect power (a square), and thus also a powerful number.

It is an interprime number because it is at equal distance from previous prime (393121) and next prime (393137).

It is not a de Polignac number, because 393129 - 2³ = 393121 is a prime.

It is an Ulam number.

393129 is a lucky number.

It is not an unprimeable number, because it can be changed into a prime (393121) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 20682 + ... + 20700.

393129 is a Friedman number, since it can be written as (33*(9+9+1))^2, using all its digits and the basic arithmetic operations.

2³⁹³¹²⁹ is an apocalyptic number.

393129 is the 627-th square number.

393129 is the 314-th centered octagonal number.

It is an amenable number.

393129 is a deficient number, since it is larger than the sum of its proper divisors (265620).

393129 is a wasteful number, since it uses less digits than its factorization.

393129 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 66 (or 33 counting only the distinct ones).

The product of its digits is 1458, while the sum is 27.

The cubic root of 393129 is about 73.2563080140.

The spelling of 393129 in words is "three hundred ninety-three thousand, one hundred twenty-nine".