72513 has 12 divisors (see below), whose sum is σ = 119808. Its totient is φ = 41400.

The previous prime is 72503. The next prime is 72533. The reversal of 72513 is 31527.

It is not a de Polignac number, because 72513 - 2⁴ = 72497 is a prime.

It is a hoax number, since the sum of its digits (18) coincides with the sum of the digits of its distinct prime factors.

It is not an unprimeable number, because it can be changed into a prime (72503) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 513 + ... + 638.

It is an arithmetic number, because the mean of its divisors is an integer number (9984).

2⁷²⁵¹³ is an apocalyptic number.

It is an amenable number.

72513 is a deficient number, since it is larger than the sum of its proper divisors (47295).

72513 is a wasteful number, since it uses less digits than its factorization.

72513 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1164 (or 1161 counting only the distinct ones).

The product of its digits is 210, while the sum is 18.

The square root of 72513 is about 269.2823796686. The cubic root of 72513 is about 41.7002467076.

It can be divided in two parts, 72 and 513, that added together give a palindrome (585).

The spelling of 72513 in words is "seventy-two thousand, five hundred thirteen".