101312133102000 has 640 divisors, whose sum is σ = 365589088300800. Its totient is φ = 26818615296000.

The previous prime is 101312133101941. The next prime is 101312133102017. The reversal of 101312133102000 is 201331213101.

101312133102000 is a `hidden beast` number, since 1 + 0 + 1 + 312 + 1 + 331 + 0 + 20 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 5561396892 + ... + 5561415108.

It is an arithmetic number, because the mean of its divisors is an integer number (571232950470).

Almost surely, 2^{101312133102000} is an apocalyptic number.

101312133102000 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 101312133102000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (182794544150400).

101312133102000 is an abundant number, since it is smaller than the sum of its proper divisors (264276955198800).

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

101312133102000 is a wasteful number, since it uses less digits than its factorization.

101312133102000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 18999 (or 18977 counting only the distinct ones).

The product of its (nonzero) digits is 108, while the sum is 18.

Adding to 101312133102000 its reverse (201331213101), we get a palindrome (101513464315101).

The spelling of 101312133102000 in words is "one hundred one trillion, three hundred twelve billion, one hundred thirty-three million, one hundred two thousand".