513 has 8 divisors (see below), whose sum is σ = 800. Its totient is φ = 324.

The previous prime is 509. The next prime is 521. The reversal of 513 is 315.

513 is nontrivially palindromic in base 2 and base 8.

It is a Cunningham number, because it is equal to 2⁹+1.

It is not a de Polignac number, because 513 - 2² = 509 is a prime.

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

It is a Duffinian number.

It is a plaindrome in base 12 and base 14.

It is a nialpdrome in base 9.

It is a junction number, because it is equal to n+sod(n) for n = 495 and 504.

It is not an unprimeable number, because it can be changed into a prime (503) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 18 + ... + 36.

It is an arithmetic number, because the mean of its divisors is an integer number (100).

It is a Proth number, since it is equal to 1 ⋅ 2⁹ + 1 and 1 < 2⁹.

It is an amenable number.

513 is a deficient number, since it is larger than the sum of its proper divisors (287).

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

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

The sum of its prime factors is 28 (or 22 counting only the distinct ones).

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

The square root of 513 is about 22.6495033058. The cubic root of 513 is about 8.0052049462.

Adding to 513 its product of digits (15), we get a triangular number (528 = T₃₂).

Adding to 513 its reverse (315), we get a palindrome (828).

It can be divided in two parts, 51 and 3, that multiplied together give a triangular number (153 = T₁₇).

The spelling of 513 in words is "five hundred thirteen", and thus it is an aban number and an oban number.