414388128 has 192 divisors, whose sum is σ = 1379911680. Its totient is φ = 105753600.

The previous prime is 414388109. The next prime is 414388133. The reversal of 414388128 is 821883414.

It is a happy number.

It is a nude number because it is divisible by every one of its digits.

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 31 ways as a sum of consecutive naturals, for example, 450453 + ... + 451371.

It is an arithmetic number, because the mean of its divisors is an integer number (7187040).

Almost surely, 2^414388128 is an apocalyptic number.

414388128 is a gapful number since it is divisible by the number (48) 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 414388128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (689955840).

414388128 is an abundant number, since it is smaller than the sum of its proper divisors (965523552).

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

414388128 is a wasteful number, since it uses less digits than its factorization.

414388128 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1011 (or 1003 counting only the distinct ones).

The product of its digits is 49152, while the sum is 39.

The square root of 414388128 is about 20356.5254402612. The cubic root of 414388128 is about 745.5368279228.

The spelling of 414388128 in words is "four hundred fourteen million, three hundred eighty-eight thousand, one hundred twenty-eight".