101125908009 has 81 divisors (see below), whose sum is σ = 179558132247. Its totient is φ = 54676163808.

The previous prime is 101125907999. The next prime is 101125908017. The reversal of 101125908009 is 900809521101.

101125908009 = 1³ + 2³ + ... + 797³.

The square root of 101125908009 is 318003.

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., 49037888025 + 52088019984 = 221445^2 + 228228^2 .

It is not a de Polignac number, because 101125908009 - 2¹⁵ = 101125875241 is a prime.

It is not an unprimeable number, because it can be changed into a prime (101125908049) 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 80 ways as a sum of consecutive naturals, for example, 126882799 + ... + 126883595.

Almost surely, 2^101125908009 is an apocalyptic number.

101125908009 is a gapful number since it is divisible by the number (19) formed by its first and last digit.

101125908009 is the 318003-rd square number.

101125908009 is the 159002-nd centered octagonal number.

It is an amenable number.

101125908009 is a deficient number, since it is larger than the sum of its proper divisors (78432224238).

101125908009 is an frugal number, since it uses more digits than its factorization.

101125908009 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1652 (or 826 counting only the distinct ones).

The product of its (nonzero) digits is 6480, while the sum is 36.

Multiplying 101125908009 by its sum of digits (36), we get a square (3640532688324 = 1908018²).

The spelling of 101125908009 in words is "one hundred one billion, one hundred twenty-five million, nine hundred eight thousand, nine".