81771870128400 has 405 divisors, whose sum is σ = 293950296811821. Its totient is φ = 21049855626240.

The previous prime is 81771870128393. The next prime is 81771870128449. The reversal of 81771870128400 is 482107817718.

It is a happy number.

The square root of 81771870128400 is 9042780.

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

81771870128400 is a `hidden beast` number, since 81 + 7 + 71 + 8 + 70 + 1 + 28 + 400 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 53755936440336 + 28015933688064 = 7331844^2 + 5293008^2 .

It is an unprimeable number.

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 80 ways as a sum of consecutive naturals, for example, 15734434602 + ... + 15734439798.

Almost surely, 2^{81771870128400} is an apocalyptic number.

81771870128400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

81771870128400 is the 9042780-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 81771870128400

81771870128400 is an abundant number, since it is smaller than the sum of its proper divisors (212178426683421).

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

81771870128400 is an equidigital number, since it uses as much as digits as its factorization.

81771870128400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10476 (or 5236 counting only the distinct ones).

The product of its (nonzero) digits is 1404928, while the sum is 54.

The spelling of 81771870128400 in words is "eighty-one trillion, seven hundred seventy-one billion, eight hundred seventy million, one hundred twenty-eight thousand, four hundred".