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56 (number)

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Natural number

56

←50 51 52 53 54 55 56 57 58 59 →

←0 10 20 30 40 50 60 70 80 90 →

fifty-six

56th
(fifty-sixth)

2³ × 7

1, 2, 4, 7, 8, 14, 28, 56

ΝϚ´

LVI,lvi

111000₂

2002₃

132₆

70₈

48₁₂

38₁₆

56 (fifty-six) is thenatural number following55 and preceding57.

Mathematics

Regular 56-gon, associated by the Pythagoreans withTyphon

56 is:

The sum of the first sixtriangular numbers (making it atetrahedral number).^[1]
The number of ways to choose 3 out of 8 objects or 5 out of 8 objects, if order does not matter.
The sum of six consecutiveprimes (3 + 5 + 7 + 11 + 13 + 17)
atetranacci number^[2] and as a multiple of 7 and 8, apronic number.^[3] It is one of a few pronic numbers whose digits in decimal also are successive (5 and 6).
arefactorable number, since 8 is one of its 8 divisors.
The sum of the sums of the divisors of the first 8positive integers.^[4]
Asemiperfect number, since 56 is twicea perfect number.
Apartition number – the number of distinct ways 11 can be represented as the sum of natural numbers.
AnErdős–Woods number, since it is possible to find sequences of 56 consecutive integers such that each inner member shares a factor with either the first or the last member.^[5]
The only known number n such thatφ(n − 1)σ(n − 1) = φ(n)σ(n) = φ(n + 1)σ(n + 1), where φ(m) isEuler's totient function and σ(n) is thesum of the divisor function, seeOEIS: A244439.
Themaximum determinant in an 8 by 8matrix of zeroes and ones.
The number ofpolygons formed by connecting all the 8 points on the perimeter of a two-times-two-square by straight lines.^[6]

Plutarch^[7] states that thePythagoreans associated a polygon of 56 sides withTyphon and that they associated certain polygons of smaller numbers of sides with other figures in Greek mythology. While it is impossible to construct a perfect regular 56-sided polygon using a compass and straightedge, a close approximation has recently been discovered which it is claimed^[8] might have been used at Stonehenge, and it is constructible if the use of anangle trisector is allowed since 56 = 2³ × 7.^[9]

Organizations

The symbol of theHungarian Revolution of 1956.
Brazilian politicianEnéas Carneiro has an odd way of repeating the number of his party, "Fifty-Six" (cinquenta e seis, inPortuguese), making it a widely repeated jargon in his country.

References

^Sloane, N. J. A. (ed.)."Sequence A000292 (Tetrahedral numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-30.
^Sloane, N. J. A. (ed.)."Sequence A000078 (Tetranacci numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-30.
^Sloane, N. J. A. (ed.)."Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-30.
^Sloane, N. J. A. (ed.)."Sequence A024916 (sum_{k=1..n} sigma(k) where sigma(n) = sum of divisors of n)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^Sloane, N. J. A. (ed.)."Sequence A059756 (Erdős-Woods numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-30.
^Sloane, N. J. A. (ed.)."Sequence A255011".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2022-05-09.
^Plutarch,Moralia V: 30
^Pegs and Ropes: Geometry at Stonehenge
^"Constructibility of Regular Polygons"(PDF). Archived fromthe original(PDF) on 2015-07-14. Retrieved2015-02-19.

v
t
e

\mathbb {Z}

−2,−1

0 to 199

0 to 99	100 to 199
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99	100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199

200 to 399

200 to 299	300 to 399
200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299	300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399

400 to 999

400s, 500s, and 600s	700s, 800s, and 900s
400 420 440 495 496 500 501 511 512 555 600 610 613 616 666 693	700 720 743 744 777 786 800 801 836 840 880 881 888 900 911 971 987 999

1000s and 10,000s
1000s	1000 1001 1023 1024 1089 1093 1105 1234 1289 1458 1510 1728 1729 1980 1987 2000 2016 2520 3000 3511 4000 4104 5000 5040 6000 6174 7000 7744 7825 8000 8128 8192 9000 9855 9999
10,000s	10,000 16,807 20,000 30,000 40,000 50,000 60,000 64,079 65,535 65,536 65,537 70,000 80,000 90,000

100,000s to 10,000,000,000,000s
100,000 142,857 144,000 1,000,000 10,000,000 43,112,609 100,000,000 1,000,000,000 2,147,483,647 4,294,967,295 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000

Large numbers

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Integers

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