820972403643456 has 637 divisors, whose sum is σ = 2596403764749649. Its totient is φ = 257559969770496.

The previous prime is 820972403643391. The next prime is 820972403643493. The reversal of 820972403643456 is 654346304279028.

It is a happy number.

The square root of 820972403643456 is 28652616.

The cubic root of 820972403643456 is 93636.

It is a perfect power (a square, a cube, a 6-th power), and thus also a powerful number.

820972403643456 is a `hidden beast` number, since 8 + 2 + 0 + 9 + 72 + 40 + 36 + 43 + 456 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 8333845185600 + 812638558457856 = 2886840^2 + 28506816^2 .

It is a super-2 number, since 2×820972403643456² (a number of 31 digits) contains 22 as substring.

It is a Duffinian number.

It is a junction number, because it is equal to n+sod(n) for n = 820972403643393 and 820972403643402.

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 90 ways as a sum of consecutive naturals, for example, 48292494331960 + ... + 48292494331976.

Almost surely, 2^{820972403643456} is an apocalyptic number.

820972403643456 is the 28652616-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 820972403643456

820972403643456 is an abundant number, since it is smaller than the sum of its proper divisors (1775431361106193).

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

820972403643456 is an frugal number, since it uses more digits than its factorization.

820972403643456 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 150 (or 22 counting only the distinct ones).

The product of its (nonzero) digits is 209018880, while the sum is 63.

The spelling of 820972403643456 in words is "eight hundred twenty trillion, nine hundred seventy-two billion, four hundred three million, six hundred forty-three thousand, four hundred fifty-six".