509217408 has 384 divisors, whose sum is σ = 1823270400. Its totient is φ = 139345920.

The previous prime is 509217407. The next prime is 509217419. The reversal of 509217408 is 804712905.

It is a tau number, because it is divible by the number of its divisors (384).

It is a super-2 number, since 2×509217408² = 518604737220476928, which contains 22 as substring.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (509217407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 5249616 + ... + 5249712.

It is an arithmetic number, because the mean of its divisors is an integer number (4748100).

Almost surely, 2^509217408 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 509217408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (911635200).

509217408 is an abundant number, since it is smaller than the sum of its proper divisors (1314052992).

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

509217408 is a wasteful number, since it uses less digits than its factorization.

509217408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 165 (or 140 counting only the distinct ones).

The product of its (nonzero) digits is 20160, while the sum is 36.

The square root of 509217408 is about 22565.8460510569. The cubic root of 509217408 is about 798.5480999101.

It can be divided in two parts, 5092 and 17408, that added together give a square (22500 = 150²).

The spelling of 509217408 in words is "five hundred nine million, two hundred seventeen thousand, four hundred eight".