4004000 has 192 divisors, whose sum is σ = 13208832. Its totient is φ = 1152000.

The previous prime is 4003999. The next prime is 4004009. The reversal of 4004000 is 4004.

Added to its reverse (4004) it gives a square (4008004 = 2002²).

It is a happy number.

It is a Cunningham number, because it is equal to 2001²-1.

It is a Harshad number since it is a multiple of its sum of digits (8).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (4004009) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 307994 + ... + 308006.

It is an arithmetic number, because the mean of its divisors is an integer number (68796).

Almost surely, 2^4004000 is an apocalyptic number.

4004000 is a gapful number since it is divisible by the number (40) 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 4004000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6604416).

4004000 is an abundant number, since it is smaller than the sum of its proper divisors (9204832).

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

4004000 is a wasteful number, since it uses less digits than its factorization.

4004000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 56 (or 38 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 8.

The square root of 4004000 is about 2000.9997501249. Note that the first 3 decimals coincide. The cubic root of 4004000 is about 158.7930009372.

Adding to 4004000 its reverse (4004), we get a palindrome (4008004).

4004000 divided by its reverse (4004) gives a cube (1000 = 10³).

The spelling of 4004000 in words is "four million, four thousand", and thus it is an eban number.