513205 has 32 divisors (see below), whose sum is σ = 811008. Its totient is φ = 302400.

The previous prime is 513203. The next prime is 513239. The reversal of 513205 is 502315.

513205 = 11² + 12² + ... + 115².

513205 is nontrivially palindromic in base 6.

It is not a de Polignac number, because 513205 - 2¹ = 513203 is a prime.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513203) 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, 11914 + ... + 11956.

It is an arithmetic number, because the mean of its divisors is an integer number (25344).

2⁵¹³²⁰⁵ is an apocalyptic number.

513205 is a gapful number since it is divisible by the number (55) formed by its first and last digit.

It is an amenable number.

513205 is a deficient number, since it is larger than the sum of its proper divisors (297803).

513205 is a wasteful number, since it uses less digits than its factorization.

513205 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 97.

The product of its (nonzero) digits is 150, while the sum is 16.

The square root of 513205 is about 716.3832773034. The cubic root of 513205 is about 80.0627112451.

The spelling of 513205 in words is "five hundred thirteen thousand, two hundred five".