31752 has 60 divisors (see below), whose sum is σ = 103455. Its totient is φ = 9072.

The previous prime is 31751. The next prime is 31769. The reversal of 31752 is 25713.

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.

31752 is nontrivially palindromic in base 5.

It can be written as a sum of positive squares in only one way, i.e., 15876 + 15876 = 126^2 + 126^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=126.

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

It is a nialpdrome in base 14.

It is not an unprimeable number, because it can be changed into a prime (31751) by changing a digit.

It is a polite number, since it can be written in 14 ways as a sum of consecutive naturals, for example, 4533 + ... + 4539.

2^{31752} 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 31752

31752 is an abundant number, since it is smaller than the sum of its proper divisors (71703).

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

31752 is a wasteful number, since it uses less digits than its factorization.

31752 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 32 (or 12 counting only the distinct ones).

The product of its digits is 210, while the sum is 18.

The square root of 31752 is about 178.1909088590. The cubic root of 31752 is about 31.6657925274.

Multiplying 31752 by its sum of digits (18), we get a square (571536 = 756^{2}).

31752 divided by its sum of digits (18) gives a square (1764 = 42^{2}).

The spelling of 31752 in words is "thirty-one thousand, seven hundred fifty-two".

Divisors: 1 2 3 4 6 7 8 9 12 14 18 21 24 27 28 36 42 49 54 56 63 72 81 84 98 108 126 147 162 168 189 196 216 252 294 324 378 392 441 504 567 588 648 756 882 1134 1176 1323 1512 1764 2268 2646 3528 3969 4536 5292 7938 10584 15876 31752

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