509984 has 12 divisors (see below), whose sum is σ = 1004094. Its totient is φ = 254976.

The previous prime is 509963. The next prime is 509989. The reversal of 509984 is 489905.

It can be written as a sum of positive squares in only one way, i.e., 394384 + 115600 = 628^2 + 340^2 .

It is a Smith number, since the sum of its digits (35) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (509989) by changing a digit.

509984 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 7937 + ... + 8000.

2⁵⁰⁹⁹⁸⁴ is an apocalyptic number.

It is an amenable number.

509984 is a deficient number, since it is larger than the sum of its proper divisors (494110).

509984 is a wasteful number, since it uses less digits than its factorization.

509984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 15947 (or 15939 counting only the distinct ones).

The product of its (nonzero) digits is 12960, while the sum is 35.

The square root of 509984 is about 714.1316405258. The cubic root of 509984 is about 79.8948618852.

The spelling of 509984 in words is "five hundred nine thousand, nine hundred eighty-four".