10000001101001 has 16 divisors (see below), whose sum is σ = 10099447318800. Its totient is φ = 9901007339520.

The previous prime is 10000001100983. The next prime is 10000001101009. The reversal of 10000001101001 is 10010110000001.

It can be written as a sum of positive squares in 8 ways, for example, as 53325893776 + 9946675207225 = 230924^2 + 3153835^2 .

It is a cyclic number.

It is not a de Polignac number, because 10000001101001 - 2²⁶ = 9999933992137 is a prime.

It is a Duffinian number.

It is a Curzon number.

It is not an unprimeable number, because it can be changed into a prime (10000001101009) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 144765011 + ... + 144834071.

It is an arithmetic number, because the mean of its divisors is an integer number (631215457425).

Almost surely, 2^{10000001101001} is an apocalyptic number.

It is an amenable number.

10000001101001 is a deficient number, since it is larger than the sum of its proper divisors (99446217799).

10000001101001 is a wasteful number, since it uses less digits than its factorization.

10000001101001 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 72316.

The product of its (nonzero) digits is 1, while the sum is 5.

Adding to 10000001101001 its reverse (10010110000001), we get a palindrome (20010111101002).

The spelling of 10000001101001 in words is "ten trillion, one million, one hundred one thousand, one".