73728 has 42 divisors (see below), whose sum is σ = 212979. Its totient is φ = 24576.

The previous prime is 73727. The next prime is 73751. The reversal of 73728 is 82737.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as (4!)^{2} ⋅ (2!)^{7}.

It can be written as a sum of positive squares in only one way, i.e., 36864 + 36864 = 192^2 + 192^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=192.

It is a nialpdrome in base 8.

It is a zygodrome in base 8.

It is not an unprimeable number, because it can be changed into a prime (73721) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 24575 + 24576 + 24577.

2^{73728} 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 73728

73728 is an abundant number, since it is smaller than the sum of its proper divisors (139251).

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

73728 is an equidigital number, since it uses as much as digits as its factorization.

73728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 5 counting only the distinct ones).

The product of its digits is 2352, while the sum is 27.

The square root of 73728 is about 271.5290039756. The cubic root of 73728 is about 41.9318623073.

Subtracting 73728 from its reverse (82737), we obtain a palindrome (9009).

The spelling of 73728 in words is "seventy-three thousand, seven hundred twenty-eight".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 32 36 48 64 72 96 128 144 192 256 288 384 512 576 768 1024 1152 1536 2048 2304 3072 4096 4608 6144 8192 9216 12288 18432 24576 36864 73728

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