509856 has 48 divisors (see below), whose sum is σ = 1378944. Its totient is φ = 164864.

The previous prime is 509843. The next prime is 509863. The reversal of 509856 is 658905.

509856 = 234² + 235² + ... + 242².

It is a tau number, because it is divible by the number of its divisors (48).

It is an alternating number because its digits alternate between odd and even.

It is an unprimeable number.

509856 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 4456 + ... + 4568.

It is an arithmetic number, because the mean of its divisors is an integer number (28728).

2⁵⁰⁹⁸⁵⁶ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 509856, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (689472).

509856 is an abundant number, since it is smaller than the sum of its proper divisors (869088).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

509856 is a wasteful number, since it uses less digits than its factorization.

509856 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 173 (or 165 counting only the distinct ones).

The product of its (nonzero) digits is 10800, while the sum is 33.

The square root of 509856 is about 714.0420155705. The cubic root of 509856 is about 79.8881771017. Note that the first 3 decimals are identical.

The spelling of 509856 in words is "five hundred nine thousand, eight hundred fifty-six".