384134400 has 648 divisors, whose sum is σ = 1614514720. Its totient is φ = 89579520.

The previous prime is 384134369. The next prime is 384134461. The reversal of 384134400 is 4431483.

It is a tau number, because it is divible by the number of its divisors (648).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 20217591 + ... + 20217609.

Almost surely, 2^384134400 is an apocalyptic number.

384134400 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 384134400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (807257360).

384134400 is an abundant number, since it is smaller than the sum of its proper divisors (1230380320).

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

384134400 is a wasteful number, since it uses less digits than its factorization.

384134400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 73 (or 42 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 27.

The square root of 384134400 is about 19599.3469278953. The cubic root of 384134400 is about 726.9330262026.

Adding to 384134400 its reverse (4431483), we get a palindrome (388565883).

The spelling of 384134400 in words is "three hundred eighty-four million, one hundred thirty-four thousand, four hundred".