20736 has 45 divisors (see below), whose sum is σ = 61831. Its totient is φ = 6912.

The previous prime is 20731. The next prime is 20743. The reversal of 20736 is 63702.

20736 = T_{143} + T_{144}.

The square root of 20736 is 144.

It is a perfect power (a square, a biquadrate), and thus also a powerful number.

It is a Jordan-Polya number, since it can be written as (4!)^{2} ⋅ (3!)^{2}.

20736 is nontrivially palindromic in base 11 and base 15.

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

It is an Ulam number.

It is a Duffinian number.

It is a nialpdrome in base 12 and base 16.

It is not an unprimeable number, because it can be changed into a prime (20731) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 4 ways as a sum of consecutive naturals, for example, 6911 + 6912 + 6913.

20736 is a Friedman number, since it can be written as (2*(6+0))^(7-3), using all its digits and the basic arithmetic operations.

2^{20736} is an apocalyptic number.

20736 is the 144-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 20736

20736 is an abundant number, since it is smaller than the sum of its proper divisors (41095).

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

20736 is an frugal number, since it uses more digits than its factorization.

20736 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 28 (or 5 counting only the distinct ones).

The product of its (nonzero) digits is 252, while the sum is 18.

The cubic root of 20736 is about 27.4731418213.

Multiplying 20736 by its sum of digits (18), we get a cube (373248 = 72^{3}).

It can be divided in two parts, 207 and 36, that added together give a 5-th power (243 = 3^{5}).

The spelling of 20736 in words is "twenty thousand, seven hundred thirty-six".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192 216 256 288 324 384 432 576 648 768 864 1152 1296 1728 2304 2592 3456 5184 6912 10368 20736

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