101605681800 has 768 divisors, whose sum is σ = 421044480000. Its totient is φ = 22029235200.

The previous prime is 101605681739. The next prime is 101605681817. The reversal of 101605681800 is 8186506101.

101605681800 is a `hidden beast` number, since 1 + 0 + 16 + 0 + 568 + 1 + 80 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 64675015 + ... + 64676585.

It is an arithmetic number, because the mean of its divisors is an integer number (548235000).

Almost surely, 2^101605681800 is an apocalyptic number.

101605681800 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 101605681800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (210522240000).

101605681800 is an abundant number, since it is smaller than the sum of its proper divisors (319438798200).

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

101605681800 is a wasteful number, since it uses less digits than its factorization.

101605681800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1691 (or 1676 counting only the distinct ones).

The product of its (nonzero) digits is 11520, while the sum is 36.

The spelling of 101605681800 in words is "one hundred one billion, six hundred five million, six hundred eighty-one thousand, eight hundred".