105385142016 has 864 divisors, whose sum is σ = 401768640000. Its totient is φ = 27311800320.

The previous prime is 105385142003. The next prime is 105385142047. The reversal of 105385142016 is 610241583501.

105385142016 is a `hidden beast` number, since 105 + 3 + 8 + 514 + 20 + 16 = 666.

It is a tau number, because it is divible by the number of its divisors (864).

It is a super-2 number, since 2×105385142016² (a number of 23 digits) contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 234710560 + ... + 234711008.

It is an arithmetic number, because the mean of its divisors is an integer number (465010000).

Almost surely, 2^105385142016 is an apocalyptic number.

105385142016 is a gapful number since it is divisible by the number (16) 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 105385142016, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (200884320000).

105385142016 is an abundant number, since it is smaller than the sum of its proper divisors (296383497984).

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

105385142016 is an frugal number, since it uses more digits than its factorization.

105385142016 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 512 (or 472 counting only the distinct ones).

The product of its (nonzero) digits is 28800, while the sum is 36.

The spelling of 105385142016 in words is "one hundred five billion, three hundred eighty-five million, one hundred forty-two thousand, sixteen".