509339142400 has 243 divisors, whose sum is σ = 1387432226649. Its totient is φ = 184985856000.

The previous prime is 509339142349. The next prime is 509339142413. The reversal of 509339142400 is 4241933905.

The square root of 509339142400 is 713680.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 183362091264 + 325977051136 = 428208^2 + 570944^2 .

It is a Harshad number since it is a multiple of its sum of digits (40).

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 628037995 + ... + 628038805.

Almost surely, 2^509339142400 is an apocalyptic number.

509339142400 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

509339142400 is the 713680-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 509339142400

509339142400 is an abundant number, since it is smaller than the sum of its proper divisors (878093084249).

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

509339142400 is an frugal number, since it uses more digits than its factorization.

509339142400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1670 (or 829 counting only the distinct ones).

The product of its (nonzero) digits is 116640, while the sum is 40.

The spelling of 509339142400 in words is "five hundred nine billion, three hundred thirty-nine million, one hundred forty-two thousand, four hundred".