1004006004001 has 125 divisors (see below), whose sum is σ = 1395751758805. Its totient is φ = 722162160720.

The previous prime is 1004006003999. The next prime is 1004006004047.

It is a happy number.

The square root of 1004006004001 is 1002001.

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

1004006004001 is nontrivially palindromic in base 10.

It can be written as a sum of positive squares in 2 ways, for example, as 497802213601 + 506203790400 = 705551^2 + 711480^2 .

It is not a de Polignac number, because 1004006004001 - 2¹ = 1004006003999 is a prime.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (1004006008001) by changing a digit.

It is a polite number, since it can be written in 124 ways as a sum of consecutive naturals, for example, 77231231071 + ... + 77231231083.

Almost surely, 2^{1004006004001} is an apocalyptic number.

1004006004001 is a gapful number since it is divisible by the number (11) formed by its first and last digit.

1004006004001 is the 1002001-st square number.

1004006004001 is the 501001-st centered octagonal number.

It is an amenable number.

1004006004001 is a deficient number, since it is larger than the sum of its proper divisors (391745754804).

1004006004001 is an frugal number, since it uses more digits than its factorization.

1004006004001 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 124 (or 31 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 16.

Multiplying 1004006004001 by its sum of digits (16), we get a 4-th power (16064096064016 = 2002⁴).

The spelling of 1004006004001 in words is "one trillion, four billion, six million, four thousand, one".