513315 has 48 divisors (see below), whose sum is σ = 1044576. Its totient is φ = 230400.

The previous prime is 513313. The next prime is 513319.

513315 = T₁₁₀ + T₁₁₁ + ... + T₁₆₃.

It is a happy number.

513315 is nontrivially palindromic in base 10.

It is not a de Polignac number, because 513315 - 2¹ = 513313 is a prime.

It is a super-3 number, since 3×513315³ = 405763633330592625, which contains 333 as substring.

It is a nude number because it is divisible by every one of its digits.

It is an Ulam number.

It is not an unprimeable number, because it can be changed into a prime (513311) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 8385 + ... + 8445.

It is an arithmetic number, because the mean of its divisors is an integer number (21762).

2⁵¹³³¹⁵ is an apocalyptic number.

513315 is a gapful number since it is divisible by the number (55) formed by its first and last digit.

513315 is an abundant number, since it is smaller than the sum of its proper divisors (531261).

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

513315 is a wasteful number, since it uses less digits than its factorization.

513315 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 100 (or 97 counting only the distinct ones).

The product of its digits is 225, while the sum is 18.

The square root of 513315 is about 716.4600477347. The cubic root of 513315 is about 80.0684310316.

It can be divided in two parts, 513 and 315, that added together give a palindrome (828).

The spelling of 513315 in words is "five hundred thirteen thousand, three hundred fifteen".