384993 has 30 divisors (see below), whose sum is σ = 675906. Its totient is φ = 217728.

The previous prime is 384973. The next prime is 385001. The reversal of 384993 is 399483.

It can be written as a sum of positive squares in only one way, i.e., 321489 + 63504 = 567^2 + 252^2 .

It is not a de Polignac number, because 384993 - 2⁵ = 384961 is a prime.

It is a super-2 number, since 2×384993² = 296439220098, which contains 22 as substring.

It is a Curzon number.

It is not an unprimeable number, because it can be changed into a prime (384913) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 3921 + ... + 4017.

2³⁸⁴⁹⁹³ is an apocalyptic number.

It is an amenable number.

384993 is a deficient number, since it is larger than the sum of its proper divisors (290913).

384993 is an equidigital number, since it uses as much as digits as its factorization.

384993 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 123 (or 107 counting only the distinct ones).

The product of its digits is 23328, while the sum is 36.

The square root of 384993 is about 620.4780415132. The cubic root of 384993 is about 72.7474225891.

Adding to 384993 its product of digits (23328), we get a square (408321 = 639²).

The spelling of 384993 in words is "three hundred eighty-four thousand, nine hundred ninety-three".