4004 has 24 divisors (see below), whose sum is σ = 9408. Its totient is φ = 1440.

The previous prime is 4003. The next prime is 4007.

4004 = T₇ + T₈ + ... + T₂₈.

It is a happy number.

4004 is nontrivially palindromic in base 10.

It is a plaindrome in base 15.

It is a nialpdrome in base 4, base 8 and base 16.

It is a junction number, because it is equal to n+sod(n) for n = 3982 and 4000.

It is not an unprimeable number, because it can be changed into a prime (4001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 302 + ... + 314.

It is an arithmetic number, because the mean of its divisors is an integer number (392).

4004 is a gapful number since it is divisible by the number (44) 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 4004, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4704).

4004 is an abundant number, since it is smaller than the sum of its proper divisors (5404).

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

4004 is a wasteful number, since it uses less digits than its factorization.

4004 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 35 (or 33 counting only the distinct ones).

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

The square root of 4004 is about 63.2771680782. The cubic root of 4004 is about 15.8793000937.

It can be divided in two parts, 400 and 4, that multiplied together give a square (1600 = 40²).

The spelling of 4004 in words is "four thousand, four", and thus it is an eban number and an iban number.