101605106000 has 80 divisors (see below), whose sum is σ = 245847248400. Its totient is φ = 40614566400.

The previous prime is 101605105919. The next prime is 101605106017. The reversal of 101605106000 is 601506101.

It is a happy number.

It can be written as a sum of positive squares in 8 ways, for example, as 10562906176 + 91042199824 = 102776^2 + 301732^2 .

It is a tau number, because it is divible by the number of its divisors (80).

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 3081602 + ... + 3114398.

It is an arithmetic number, because the mean of its divisors is an integer number (3073090605).

Almost surely, 2^101605106000 is an apocalyptic number.

101605106000 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 101605106000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (122923624200).

101605106000 is an abundant number, since it is smaller than the sum of its proper divisors (144242142400).

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

101605106000 is a wasteful number, since it uses less digits than its factorization.

101605106000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 34369 (or 34353 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 20.

The spelling of 101605106000 in words is "one hundred one billion, six hundred five million, one hundred six thousand".