1000106106100 has 72 divisors (see below), whose sum is σ = 2183088195288. Its totient is φ = 397674086400.

The previous prime is 1000106106049. The next prime is 1000106106107. The reversal of 1000106106100 is 16016010001.

It can be written as a sum of positive squares in 12 ways, for example, as 980999126116 + 19106979984 = 990454^2 + 138228^2 .

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1000106106107) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 52426164 + ... + 52445236.

It is an arithmetic number, because the mean of its divisors is an integer number (30320669379).

Almost surely, 2^{1000106106100} is an apocalyptic number.

1000106106100 is a gapful number since it is divisible by the number (10) 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 1000106106100, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1091544097644).

1000106106100 is an abundant number, since it is smaller than the sum of its proper divisors (1182982089188).

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

1000106106100 is a wasteful number, since it uses less digits than its factorization.

1000106106100 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 22165 (or 22158 counting only the distinct ones).

The product of its (nonzero) digits is 36, while the sum is 16.

The spelling of 1000106106100 in words is "one trillion, one hundred six million, one hundred six thousand, one hundred".