459972513 has 192 divisors, whose sum is σ = 970604544. Its totient is φ = 209952000.

The previous prime is 459972467. The next prime is 459972533. The reversal of 459972513 is 315279954.

It is a happy number.

459972513 is a `hidden beast` number, since 4 + 599 + 7 + 2 + 51 + 3 = 666.

It is not a de Polignac number, because 459972513 - 2⁶ = 459972449 is a prime.

Its product of digits (340200) is a multiple of the sum of its prime divisors (126).

It is a Curzon number.

It is not an unprimeable number, because it can be changed into a prime (459972533) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 7540503 + ... + 7540563.

It is an arithmetic number, because the mean of its divisors is an integer number (5055232).

Almost surely, 2^459972513 is an apocalyptic number.

It is an amenable number.

459972513 is an abundant number, since it is smaller than the sum of its proper divisors (510632031).

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

459972513 is a wasteful number, since it uses less digits than its factorization.

459972513 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 138 (or 126 counting only the distinct ones).

The product of its digits is 340200, while the sum is 45.

The square root of 459972513 is about 21446.9697859628. The cubic root of 459972513 is about 771.9288869546.

The spelling of 459972513 in words is "four hundred fifty-nine million, nine hundred seventy-two thousand, five hundred thirteen".