101409856128 has 192 divisors, whose sum is σ = 334475968320. Its totient is φ = 28889948160.

The previous prime is 101409856123. The next prime is 101409856147. The reversal of 101409856128 is 821658904101.

It is a happy number.

101409856128 is a `hidden beast` number, since 10 + 14 + 0 + 9 + 8 + 5 + 612 + 8 = 666.

It is a tau number, because it is divible by the number of its divisors (192).

It is not an unprimeable number, because it can be changed into a prime (101409856123) 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, 2780088 + ... + 2816328.

It is an arithmetic number, because the mean of its divisors is an integer number (1742062335).

Almost surely, 2^101409856128 is an apocalyptic number.

101409856128 is a gapful number since it is divisible by the number (18) 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 101409856128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (167237984160).

101409856128 is an abundant number, since it is smaller than the sum of its proper divisors (233066112192).

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

101409856128 is a wasteful number, since it uses less digits than its factorization.

101409856128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 36615 (or 36600 counting only the distinct ones).

The product of its (nonzero) digits is 138240, while the sum is 45.

The spelling of 101409856128 in words is "one hundred one billion, four hundred nine million, eight hundred fifty-six thousand, one hundred twenty-eight".