81648 has 70 divisors (see below), whose sum is σ = 271064. Its totient is φ = 23328.

The previous prime is 81647. The next prime is 81649. The reversal of 81648 is 84618.

It is an interprime number because it is at equal distance from previous prime (81647) and next prime (81649).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits.

Its product of digits (1536) is a multiple of the sum of its prime divisors (12).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (81647) by changing a digit.

It is a polite number, since it can be written in 13 ways as a sum of consecutive naturals, for example, 11661 + ... + 11667.

81648 is a Friedman number, since it can be written as 6^4*(8*8-1), using all its digits and the basic arithmetic operations.

2^{81648} 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 81648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (135532).

81648 is an abundant number, since it is smaller than the sum of its proper divisors (189416).

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

81648 is an equidigital number, since it uses as much as digits as its factorization.

81648 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 33 (or 12 counting only the distinct ones).

The product of its digits is 1536, while the sum is 27.

The square root of 81648 is about 285.7411415950. The cubic root of 81648 is about 43.3825607552.

It can be divided in two parts, 81 and 648, that added together give a 6-th power (729 = 3^{6}).

The spelling of 81648 in words is "eighty-one thousand, six hundred forty-eight".

Divisors: 1 2 3 4 6 7 8 9 12 14 16 18 21 24 27 28 36 42 48 54 56 63 72 81 84 108 112 126 144 162 168 189 216 243 252 324 336 378 432 486 504 567 648 729 756 972 1008 1134 1296 1458 1512 1701 1944 2268 2916 3024 3402 3888 4536 5103 5832 6804 9072 10206 11664 13608 20412 27216 40824 81648

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