105199156408896 has 189 divisors, whose sum is σ = 331447155574899. Its totient is φ = 31877711712000.

The previous prime is 105199156408891. The next prime is 105199156408897. The reversal of 105199156408896 is 698804651991501.

The square root of 105199156408896 is 10256664.

It is a perfect power (a square), and thus also a powerful number.

105199156408896 is a `hidden beast` number, since 1 + 0 + 5 + 1 + 9 + 91 + 56 + 408 + 89 + 6 = 666.

It is a super-2 number, since 2×105199156408896² (a number of 29 digits) contains 22 as substring.

It is a Smith number, since the sum of its digits (72) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (72).

It is not an unprimeable number, because it can be changed into a prime (105199156408891) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 2707739871 + ... + 2707778721.

Almost surely, 2^{105199156408896} is an apocalyptic number.

105199156408896 is a gapful number since it is divisible by the number (16) formed by its first and last digit.

105199156408896 is the 10256664-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 105199156408896

105199156408896 is an abundant number, since it is smaller than the sum of its proper divisors (226247999166003).

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

105199156408896 is an frugal number, since it uses more digits than its factorization.

105199156408896 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 77742 (or 38867 counting only the distinct ones).

The product of its (nonzero) digits is 167961600, while the sum is 72.

The spelling of 105199156408896 in words is "one hundred five trillion, one hundred ninety-nine billion, one hundred fifty-six million, four hundred eight thousand, eight hundred ninety-six".