28 (number) - Wikipedia

For the card game, see Twenty-eight (card game). Natural number

← 27 28 29 →
← 20 21 22 23 24 25 26 27 28 29 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	twenty-eight
Ordinal	28th(twenty-eighth)
Factorization	22 × 7
Divisors	1, 2, 4, 7, 14, 28
Greek numeral	ΚΗ´
Roman numeral	XXVIII, xxviii
Binary	111002
Ternary	10013
Senary	446
Octal	348
Duodecimal	2412
Hexadecimal	1C16

28 (twenty-eight) is the natural number following 27 and preceding 29.

In mathematics

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Twenty-eight is a composite number and the second perfect number as it is the sum of its proper divisors: 1 + 2 + 4 + 7 + 14 = 28 {\displaystyle 1+2+4+7+14=28} . As a perfect number, it is related to the Mersenne prime 7, since 2 3 − 1 × ( 2 3 − 1 ) = 28 {\displaystyle 2^{3-1}\times (2^{3}-1)=28} . The next perfect number is 496, the previous being 6.[1]

Though perfect, 28 is not the aliquot sum of any other number other than itself; thus, it is not part of a multi-number aliquot sequence.

Twenty-eight is the sum of the totient function for the first nine integers.[2]

Since the greatest prime factor of 28 2 + 1 = 785 {\displaystyle 28^{2}+1=785} is 157, which is more than 28 twice, 28 is a Størmer number.[3]

Twenty-eight is a harmonic divisor number,[4] a happy number,[5] the 7th triangular number,[6] a hexagonal number,[7] a Leyland number of the second kind[8] ( 2 6 − 6 2 {\displaystyle 2^{6}-6^{2}} ), and a centered nonagonal number.[9]

It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these).[10]

It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its decimal digits: 2, 8, 10, 18, 28...[11]

There are 28 convex uniform honeycombs.

Twenty-eight is the only positive integer that has a unique Kayles nim-value.

Twenty-eight is the only known number that can be expressed as a sum of the first positive integers ( 1 + 2 + 3 + 4 + 5 + 6 + 7 {\displaystyle 1+2+3+4+5+6+7} ), a sum of the first primes ( 2 + 3 + 5 + 7 + 11 {\displaystyle 2+3+5+7+11} ), and a sum of the first nonprimes ( 1 + 4 + 6 + 8 + 9 {\displaystyle 1+4+6+8+9} ), and it is unlikely that any other number has this property.[12]

There are twenty-eight oriented diffeomorphism classes of manifolds homeomorphic to the 7-sphere.[citation needed]

There are 28 non-equivalent ways of expressing 1000 as the sum of two prime numbers.[13]

Twenty-eight is the smallest number that can be expressed as the sum of four nonzero squares in (at least) three ways: 5 2 + 1 2 + 1 2 + 1 2 {\displaystyle 5^{2}+1^{2}+1^{2}+1^{2}} , 4 2 + 2 2 + 2 2 + 2 2 {\displaystyle 4^{2}+2^{2}+2^{2}+2^{2}} or 3 2 + 3 2 + 3 2 + 1 2 {\displaystyle 3^{2}+3^{2}+3^{2}+1^{2}} (see image).[14][15]

In science

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• The fourth magic number in physics.

In other fields

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Twenty-eight is:

• Deriving from the 29.46 year period of Saturn's revolution around the Sun, the 28-year cycle as well as its subdivisions by 14 and 7 are supposed in astrology to mark significant turning points or sections in the course of a person's development in life. Thus, the number 28 has special significance in the culture of religious sects such as the Kadiri and the Mevlevi dervishes. The 28-beat metric pattern often used in the music compositions accompanying the main part of the Mevlevi sema ritual is called the "Devri kebir", meaning the "Big Circle" and is a reference to above astronomical facts about the year and the Saturn year.
• In Quebec, François Pérusse, in one of his best-selling Album du peuple made a parody of Wheel of Fortune in which all of the letters picked by the contestant were present 28 times. As a result, 28 became an almost mythical number used by many Quebec youths, the phrase "Y'en a 28" (There are 28 [Letters]) became a running gag still used and recognized more than 15 years later.
• Approximately the number of grams in an ounce, and used as such in commercial trade.

References

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1. ^ "Sloane's A000396 : Perfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
2. ^ "Sloane's A002088 : Sum of totient function". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
3. ^ "Sloane's A005528 : Størmer numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
4. ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
5. ^ "Sloane's A007770 : Happy numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
6. ^ "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
7. ^ "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
8. ^ Sloane, N. J. A. (ed.). "Sequence A045575 (Leyland numbers of the second kind)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
9. ^ "Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
10. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
11. ^ "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved May 31, 2016.
12. ^ "Intersection between the sums of the first positive integers, primes and non primes". mathoverflow.net. Retrieved April 2, 2018.
13. ^ Sloane, N. J. A. (ed.). "Sequence A065577 (Number of Goldbach partitions of 10^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved August 31, 2023.
14. ^ A025368
15. ^ A025359

External links

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• Prime Curios! 28 from the Prime Pages

v t e Z {\displaystyle \mathbb {Z} } Integers
−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