105641345664 has 288 divisors, whose sum is σ = 326408584320. Its totient is φ = 33974899200.

The previous prime is 105641345657. The next prime is 105641345669. The reversal of 105641345664 is 466543146501.

105641345664 is a `hidden beast` number, since 1 + 0 + 56 + 4 + 1 + 34 + 566 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×105641345664² (a number of 23 digits) contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (105641345669) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 319157979 + ... + 319158309.

It is an arithmetic number, because the mean of its divisors is an integer number (1133363140).

Almost surely, 2^105641345664 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105641345664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (163204292160).

105641345664 is an abundant number, since it is smaller than the sum of its proper divisors (220767238656).

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

105641345664 is an frugal number, since it uses more digits than its factorization.

105641345664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 722 (or 367 counting only the distinct ones).

The product of its (nonzero) digits is 1036800, while the sum is 45.

The spelling of 105641345664 in words is "one hundred five billion, six hundred forty-one million, three hundred forty-five thousand, six hundred sixty-four".