81920 has 30 divisors (see below), whose sum is σ = 196602. Its totient is φ = 32768.

The previous prime is 81919. The next prime is 81929. The reversal of 81920 is 2918.

Multipling 81920 by its sum of digits (20), we get a square (1638400 = 1280^{2}).

81920 divided by its sum of digits (20) gives a 12-th power (4096 = 2^{12}).

It can be divided in two parts, 81 and 920, that added together give a palindrome (1001).

It can be written as a sum of positive squares in only one way, i.e., 65536 + 16384 = 256^2 + 128^2 .

It is a Harshad number since it is a multiple of its sum of digits (20).

It is an Ulam number.

It is a nialpdrome in base 4.

It is a zygodrome in base 4.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 81892 and 81901.

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 81920.

It is not an unprimeable number, because it can be changed into a prime (81929) by changing a digit.

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

In principle, a polygon with 81920 sides can be constructed with ruler and compass.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 16382 + ... + 16386.

81920 is a Friedman number, since it can be written as 80*2^(9+1), using all its digits and the basic arithmetic operations.

2^{81920} is an apocalyptic number.

81920 is a gapful number since it is divisible by the number (80) 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 81920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (98301).

81920 is an abundant number, since it is smaller than the sum of its proper divisors (114682).

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

81920 is an frugal number, since it uses more digits than its factorization.

81920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 33 (or 7 counting only the distinct ones).

The product of its (nonzero) digits is 144, while the sum is 20.

The square root of 81920 is about 286.2167011200. The cubic root of 81920 is about 43.4306818655.

The spelling of 81920 in words is "eighty-one thousand, nine hundred twenty".

Divisors: 1 2 4 5 8 10 16 20 32 40 64 80 128 160 256 320 512 640 1024 1280 2048 2560 4096 5120 8192 10240 16384 20480 40960 81920

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