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216 is the cube of 6, and is the smallest cube that can be written as a sum of three positive cubes, specifically: 3 3 + 4 3 + 5 3 = 6 3.
Membership in core sequences
Even numbers
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..., 210, 212, 214, 216, 218, 220, 222, ...
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A005843
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Composite numbers
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..., 213, 214, 215, 216, 217, 218, 219, ...
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A002808
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Abundant numbers
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..., 204, 208, 210, 216, 220, 222, 224, ...
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A005101
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Cubes
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1, 8, 27, 64, 125, 216, 343, 512, 729, ...
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A000578
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Sequences pertaining to 216
Multiples of 216
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216, 432, 648, 864, 1080, 1296, 1512, 1728, 1944, 2160, 2376, 2592, ...
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Divisors of 216
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1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
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A018338
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Partitions of 216
There are 15285151248481 partitions of 216.
The Goldbach representations of 216 are 211 + 5 = 199 + 17 = 197 + 19 = 193 + 23 = 179 + 37 = 173 + 43 = 163 + 53 = 157 + 59 = 149 + 67 = 137 + 79 = 127 + 89 = 113 + 103 = 109 + 107 = 216. Notice in that last one that 107 and 109 are successive primes (see A001043 for more numbers that share this property with 216).
There are 170 subsets of the distinct divisors of 216 that add up to 216 (see A033630). These range from the trivial single element subset to more elaborate partitions like 1 + 2 + 3 + 4 + 8 + 9 + 12 + 18 + 24 + 27 + 108 = 216.
Roots and powers of 216
In the table below, irrational numbers are given truncated to eight decimal places.
TABLE GOES HERE
Values for number theoretic functions with 216 as an argument
TABLE GOES HERE
Factorization of 216 in some quadratic integer rings
As was mentioned above, 216 is the cube of 6, which in factorizes as 2 × 3. Therefore the prime factorization of 216 is 2 3 × 3 3. But in some quadratic integer rings, either 2 or 3, or both, can be further factorized.
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2 3 × 3 3
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2 3 × 3 3
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2 3 × 3 3 OR
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2 3 × 3 3
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2 3 × 3 3
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2 3 × 3 3
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2 3 × 3 3
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Representation of 216 in various bases
Base
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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13
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14
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15
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16
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17
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18
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19
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20
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Representation
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11011000
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22000
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3120
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1331
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1000
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426
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330
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260
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216
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187
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160
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138
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116
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E6
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D8
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CC
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C0
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B7
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AG
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See also
References