509313 has 16 divisors (see below), whose sum is σ = 788480. Its totient is φ = 286416.

The previous prime is 509297. The next prime is 509317. The reversal of 509313 is 313905.

It is not a de Polignac number, because 509313 - 2⁴ = 509297 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a self number, because there is not a number n which added to its sum of digits gives 509313.

It is not an unprimeable number, because it can be changed into a prime (509317) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1506 + ... + 1812.

It is an arithmetic number, because the mean of its divisors is an integer number (49280).

2⁵⁰⁹³¹³ is an apocalyptic number.

It is an amenable number.

509313 is a deficient number, since it is larger than the sum of its proper divisors (279167).

509313 is a wasteful number, since it uses less digits than its factorization.

509313 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 396.

The product of its (nonzero) digits is 405, while the sum is 21.

The square root of 509313 is about 713.6616845537. The cubic root of 509313 is about 79.8598065493.

The spelling of 509313 in words is "five hundred nine thousand, three hundred thirteen".