513000 has 128 divisors (see below), whose sum is σ = 1872000. Its totient is φ = 129600.

The previous prime is 512999. The next prime is 513001. The reversal of 513000 is 315.

It is an interprime number because it is at equal distance from previous prime (512999) and next prime (513001).

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a taxicab number since it can be written as a sum of two cubes in more than one way. Here 513000 = 10³ + 80³ = 45³ + 75³.

It is a nialpdrome in base 15.

It is not an unprimeable number, because it can be changed into a prime (513001) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 26991 + ... + 27009.

It is an arithmetic number, because the mean of its divisors is an integer number (14625).

2⁵¹³⁰⁰⁰ is an apocalyptic number.

513000 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 513000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (936000).

513000 is an abundant number, since it is smaller than the sum of its proper divisors (1359000).

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

513000 is a wasteful number, since it uses less digits than its factorization.

513000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 49 (or 29 counting only the distinct ones).

The product of its (nonzero) digits is 15, while the sum is 9.

The square root of 513000 is about 716.2401831788. The cubic root of 513000 is about 80.0520494617.

Adding to 513000 its reverse (315), we get a palindrome (513315).

The spelling of 513000 in words is "five hundred thirteen thousand".