82177128 has 192 divisors, whose sum is σ = 263577600. Its totient is φ = 22861440.

The previous prime is 82177093. The next prime is 82177153.

It is a happy number.

82177128 is nontrivially palindromic in base 10.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 82177092 and 82177101.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 647001 + ... + 647127.

It is an arithmetic number, because the mean of its divisors is an integer number (1372800).

Almost surely, 2^82177128 is an apocalyptic number.

82177128 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 82177128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131788800).

82177128 is an abundant number, since it is smaller than the sum of its proper divisors (181400472).

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

82177128 is a wasteful number, since it uses less digits than its factorization.

82177128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 212 (or 205 counting only the distinct ones).

The product of its digits is 12544, while the sum is 36.

The square root of 82177128 is about 9065.1601199317. The cubic root of 82177128 is about 434.7607404039.

The spelling of 82177128 in words is "eighty-two million, one hundred seventy-seven thousand, one hundred twenty-eight".