82065984 has 336 divisors, whose sum is σ = 301605696. Its totient is φ = 19353600.

The previous prime is 82065983. The next prime is 82066013. The reversal of 82065984 is 48956028.

It is a tau number, because it is divible by the number of its divisors (336).

It is a Smith number, since the sum of its digits (42) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (42).

It is not an unprimeable number, because it can be changed into a prime (82065983) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1345314 + ... + 1345374.

It is an arithmetic number, because the mean of its divisors is an integer number (897636).

Almost surely, 2^82065984 is an apocalyptic number.

82065984 is a gapful number since it is divisible by the number (84) 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 82065984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (150802848).

82065984 is an abundant number, since it is smaller than the sum of its proper divisors (219539712).

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

82065984 is a wasteful number, since it uses less digits than its factorization.

82065984 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 114 (or 97 counting only the distinct ones).

The product of its (nonzero) digits is 138240, while the sum is 42.

The square root of 82065984 is about 9059.0277624036. The cubic root of 82065984 is about 434.5646483366.

The spelling of 82065984 in words is "eighty-two million, sixty-five thousand, nine hundred eighty-four".