820093248100 has 243 divisors, whose sum is σ = 2201979857889. Its totient is φ = 264287385600.

The previous prime is 820093248077. The next prime is 820093248101. The reversal of 820093248100 is 1842390028.

The square root of 820093248100 is 905590.

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

It can be written as a sum of positive squares in 13 ways, for example, as 786169502244 + 33923745856 = 886662^2 + 184184^2 .

It is a super-2 number, since 2×820093248100² (a number of 25 digits) contains 22 as substring.

It is a self number, because there is not a number n which added to its sum of digits gives 820093248100.

It is not an unprimeable number, because it can be changed into a prime (820093248101) 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 80 ways as a sum of consecutive naturals, for example, 1077651720 + ... + 1077652480.

Almost surely, 2^820093248100 is an apocalyptic number.

820093248100 is the 905590-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 820093248100

820093248100 is an abundant number, since it is smaller than the sum of its proper divisors (1381886609789).

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

820093248100 is a wasteful number, since it uses less digits than its factorization.

820093248100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1584 (or 792 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 37.

The spelling of 820093248100 in words is "eight hundred twenty billion, ninety-three million, two hundred forty-eight thousand, one hundred".