82786129920 has 768 divisors, whose sum is σ = 327579033600. Its totient is φ = 19694223360.

The previous prime is 82786129913. The next prime is 82786129949. The reversal of 82786129920 is 2992168728.

82786129920 is a `hidden beast` number, since 8 + 278 + 61 + 299 + 20 = 666.

It is a tau number, because it is divible by the number of its divisors (768).

It is a super-2 number, since 2×82786129920² (a number of 23 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 111421069 + ... + 111421811.

It is an arithmetic number, because the mean of its divisors is an integer number (426535200).

Almost surely, 2^82786129920 is an apocalyptic number.

82786129920 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82786129920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (163789516800).

82786129920 is an abundant number, since it is smaller than the sum of its proper divisors (244792903680).

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

82786129920 is a wasteful number, since it uses less digits than its factorization.

82786129920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 823 (or 797 counting only the distinct ones).

The product of its (nonzero) digits is 1741824, while the sum is 54.

The spelling of 82786129920 in words is "eighty-two billion, seven hundred eighty-six million, one hundred twenty-nine thousand, nine hundred twenty".