4004001 has 27 divisors (see below), whose sum is σ = 6261619. Its totient is φ = 2465232.

The previous prime is 4003999. The next prime is 4004009. The reversal of 4004001 is 1004004.

The square root of 4004001 is 2001.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 2099601 + 1904400 = 1449^2 + 1380^2 .

It is not a de Polignac number, because 4004001 - 2¹ = 4003999 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a Duffinian 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 26 ways as a sum of consecutive naturals, for example, 138055 + ... + 138083.

Almost surely, 2^4004001 is an apocalyptic number.

4004001 is the 2001-st square number.

4004001 is the 1001-st centered octagonal number.

It is an amenable number.

4004001 is a deficient number, since it is larger than the sum of its proper divisors (2257618).

4004001 is a wasteful number, since it uses less digits than its factorization.

4004001 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 110 (or 55 counting only the distinct ones).

The product of its (nonzero) digits is 16, while the sum is 9.

The cubic root of 4004001 is about 158.7930141568.

Multiplying 4004001 by its product of nonzero digits (16), we get a square (64064016 = 8004²).

Adding to 4004001 its reverse (1004004), we get a palindrome (5008005).

Multiplying 4004001 by its reverse (1004004), we get a square (4020033020004 = 2005002²).

The spelling of 4004001 in words is "four million, four thousand, one".