163296 has 84 divisors (see below), whose sum is σ = 550872. Its totient is φ = 46656.

The previous prime is 163259. The next prime is 163307. The reversal of 163296 is 692361.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (84).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is an alternating number because its digits alternate between odd and even.

Its product of digits (1944) is a multiple of the sum of its prime divisors (12).

It is a nialpdrome in base 6.

It is a zygodrome in base 6.

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 163296.

It is an unprimeable number.

163296 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 13 ways as a sum of consecutive naturals, for example, 23325 + ... + 23331.

It is an arithmetic number, because the mean of its divisors is an integer number (6558).

163296 is a Friedman number, since it can be written as 6^6*(9/3+1/2), using all its digits and the basic arithmetic operations.

2^{163296} is an apocalyptic number.

163296 is a gapful number since it is divisible by the number (16) 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 163296, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (275436).

163296 is an abundant number, since it is smaller than the sum of its proper divisors (387576).

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

163296 is an frugal number, since it uses more digits than its factorization.

163296 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 35 (or 12 counting only the distinct ones).

The product of its digits is 1944, while the sum is 27.

The square root of 163296 is about 404.0989977716. The cubic root of 163296 is about 54.6586014938.

It can be divided in two parts, 1632 and 96, that added together give a cube (1728 = 12^{3}).

The spelling of 163296 in words is "one hundred sixty-three thousand, two hundred ninety-six".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 32 36 42 48 54 56 63 72 81 84 96 108 112 126 144 162 168 189 216 224 243 252 288 324 336 378 432 486 504 567 648 672 729 756 864 972 1008 1134 1296 1458 1512 1701 1944 2016 2268 2592 2916 3024 3402 3888 4536 5103 5832 6048 6804 7776 9072 10206 11664 13608 18144 20412 23328 27216 40824 54432 81648 163296

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