509413108320 has 576 divisors, whose sum is σ = 1941302039040. Its totient is φ = 125676085248.

The previous prime is 509413108283. The next prime is 509413108357. The reversal of 509413108320 is 23801314905.

509413108320 is a `hidden beast` number, since 509 + 4 + 13 + 108 + 32 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (509413108283) and next prime (509413108357).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 38990109 + ... + 39003171.

It is an arithmetic number, because the mean of its divisors is an integer number (3370316040).

Almost surely, 2^509413108320 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 509413108320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (970651019520).

509413108320 is an abundant number, since it is smaller than the sum of its proper divisors (1431888930720).

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

509413108320 is a wasteful number, since it uses less digits than its factorization.

509413108320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 13169 (or 13149 counting only the distinct ones).

The product of its (nonzero) digits is 25920, while the sum is 36.

The spelling of 509413108320 in words is "five hundred nine billion, four hundred thirteen million, one hundred eight thousand, three hundred twenty".