82135266253128 has 512 divisors, whose sum is σ = 270311100480000. Its totient is φ = 22829059768320.

The previous prime is 82135266253099. The next prime is 82135266253171.

82135266253128 is a `hidden beast` number, since 8 + 2 + 1 + 3 + 5 + 2 + 6 + 625 + 3 + 1 + 2 + 8 = 666.

82135266253128 is nontrivially palindromic in base 10.

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

It is an unprimeable number.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 318846876 + ... + 319104372.

It is an arithmetic number, because the mean of its divisors is an integer number (527951368125).

Almost surely, 2^{82135266253128} is an apocalyptic number.

82135266253128 is a gapful number since it is divisible by the number (88) 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 82135266253128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (135155550240000).

82135266253128 is an abundant number, since it is smaller than the sum of its proper divisors (188175834226872).

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

82135266253128 is a wasteful number, since it uses less digits than its factorization.

82135266253128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 257742 (or 257732 counting only the distinct ones).

The product of its digits is 8294400, while the sum is 54.

The spelling of 82135266253128 in words is "eighty-two trillion, one hundred thirty-five billion, two hundred sixty-six million, two hundred fifty-three thousand, one hundred twenty-eight".