93312 has 56 divisors (see below), whose sum is σ = 278715. Its totient is φ = 31104.

The previous prime is 93307. The next prime is 93319. The reversal of 93312 is 21339.

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 (3!)^{6} ⋅ 2!.

It can be written as a sum of positive squares in only one way, i.e., 46656 + 46656 = 216^2 + 216^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=216.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a Leyland number of the form 6^{6} + 6^{6}.

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 a nialpdrome in base 6.

It is not an unprimeable number, because it can be changed into a prime (93319) by changing a digit.

93312 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 6 ways as a sum of consecutive naturals, for example, 31103 + 31104 + 31105.

93312 is a Friedman number, since it can be written as 2*(9*(3+1))^3, using all its digits and the basic arithmetic operations.

2^{93312} 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 93312

93312 is an abundant number, since it is smaller than the sum of its proper divisors (185403).

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

93312 is an frugal number, since it uses more digits than its factorization.

93312 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 162, while the sum is 18.

The square root of 93312 is about 305.4701294726. The cubic root of 93312 is about 45.3571577962.

Multiplying 93312 by its sum of digits (18), we get a 8-th power (1679616 = 6^{8}).

93312 divided by its sum of digits (18) gives a square (5184 = 72^{2}).

Multiplying 93312 by its product of digits (162), we get a square (15116544 = 3888^{2}).

93312 divided by its product of digits (162) gives a square (576 = 24^{2}).

It can be divided in two parts, 9 and 3312, that added together give a triangular number (3321 = T_{81}).

The spelling of 93312 in words is "ninety-three thousand, three hundred twelve".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192 216 243 288 324 384 432 486 576 648 729 864 972 1152 1296 1458 1728 1944 2592 2916 3456 3888 5184 5832 7776 10368 11664 15552 23328 31104 46656 93312

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