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82720 = 2551147
BaseRepresentation
bin10100001100100000
311012110201
4110030200
510121340
61434544
7463111
oct241440
9135421
1082720
1157170
123ba54
132b861
1422208
151979a
hex14320

82720 has 48 divisors (see below), whose sum is σ = 217728. Its totient is φ = 29440.

The previous prime is 82699. The next prime is 82721. The reversal of 82720 is 2728.

82720 = T25 + T26 + ... + T79.

It is not an unprimeable number, because it can be changed into a prime (82721) by changing a digit.

82720 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1737 + ... + 1783.

It is an arithmetic number, because the mean of its divisors is an integer number (4536).

282720 is an apocalyptic number.

82720 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

82720 is the 235-th pentagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 82720, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (108864).

82720 is an abundant number, since it is smaller than the sum of its proper divisors (135008).

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

82720 is a wasteful number, since it uses less digits than its factorization.

82720 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 73 (or 65 counting only the distinct ones).

The product of its (nonzero) digits is 224, while the sum is 19.

The square root of 82720 is about 287.6108481960. The cubic root of 82720 is about 43.5716000556.

Adding to 82720 its product of nonzero digits (224), we get a square (82944 = 2882).

The spelling of 82720 in words is "eighty-two thousand, seven hundred twenty".

Divisors: 1 2 4 5 8 10 11 16 20 22 32 40 44 47 55 80 88 94 110 160 176 188 220 235 352 376 440 470 517 752 880 940 1034 1504 1760 1880 2068 2585 3760 4136 5170 7520 8272 10340 16544 20680 41360 82720