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82416 = 24317101
BaseRepresentation
bin10100000111110000
311012001110
4110013300
510114131
61433320
7462165
oct240760
9135043
1082416
1156a14
123b840
132b689
142206c
1519646
hex141f0

82416 has 40 divisors (see below), whose sum is σ = 227664. Its totient is φ = 25600.

The previous prime is 82393. The next prime is 82421. The reversal of 82416 is 61428.

It is a Smith number, since the sum of its digits (21) coincides with the sum of the digits of its prime factors.

It is a nude number because it is divisible by every one of its digits.

It is one of the 548 Lynch-Bell numbers.

It is a junction number, because it is equal to n+sod(n) for n = 82392 and 82401.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 82416.

It is an unprimeable number.

82416 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 766 + ... + 866.

282416 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (113832).

82416 is an abundant number, since it is smaller than the sum of its proper divisors (145248).

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

82416 is a wasteful number, since it uses less digits than its factorization.

82416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 129 (or 123 counting only the distinct ones).

The product of its digits is 384, while the sum is 21.

The square root of 82416 is about 287.0818698560. The cubic root of 82416 is about 43.5181586231.

The spelling of 82416 in words is "eighty-two thousand, four hundred sixteen".

Divisors: 1 2 3 4 6 8 12 16 17 24 34 48 51 68 101 102 136 202 204 272 303 404 408 606 808 816 1212 1616 1717 2424 3434 4848 5151 6868 10302 13736 20604 27472 41208 82416