509938416 has 320 divisors, whose sum is σ = 1708224000. Its totient is φ = 146126592.

The previous prime is 509938399. The next prime is 509938417. The reversal of 509938416 is 614839905.

It is a happy number.

It is a super-2 number, since 2×509938416² = 520074376225178112, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (509938417) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 8642995 + ... + 8643053.

It is an arithmetic number, because the mean of its divisors is an integer number (5338200).

Almost surely, 2^509938416 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 509938416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (854112000).

509938416 is an abundant number, since it is smaller than the sum of its proper divisors (1198285584).

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

509938416 is a wasteful number, since it uses less digits than its factorization.

509938416 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 120 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 233280, while the sum is 45.

The square root of 509938416 is about 22581.8160474307. The cubic root of 509938416 is about 798.9248139494.

The spelling of 509938416 in words is "five hundred nine million, nine hundred thirty-eight thousand, four hundred sixteen".