4000004000001 has 9 divisors (see below), whose sum is σ = 5777792222241. Its totient is φ = 2666665333332.

The previous prime is 4000003999951. The next prime is 4000004000017. The reversal of 4000004000001 is 1000004000004.

The square root of 4000004000001 is 2000001.

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

It is a tau number, because it is divible by the number of its divisors (9).

It is not a de Polignac number, because 4000004000001 - 2²¹ = 4000001902849 is a prime.

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

It is not an unprimeable number, because it can be changed into a prime (4000004000401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 5666670 + ... + 6333336.

Almost surely, 2^{4000004000001} is an apocalyptic number.

4000004000001 is the 2000001-st square number.

4000004000001 is the 1000001-st centered octagonal number.

It is an amenable number.

4000004000001 is a deficient number, since it is larger than the sum of its proper divisors (1777788222240).

4000004000001 is an frugal number, since it uses more digits than its factorization.

4000004000001 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1333340 (or 666670 counting only the distinct ones).

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

Multiplying 4000004000001 by its product of nonzero digits (16), we get a square (64000064000016 = 8000004²).

Adding to 4000004000001 its reverse (1000004000004), we get a palindrome (5000008000005).

The spelling of 4000004000001 in words is "four trillion, four million, one", and thus it is an aban number.