# 280 (number)

(Redirected from 288 (number))
 ← 279 280 281 →
Cardinal two hundred eighty
Ordinal 280th
(two hundred eightieth)
Factorization 5 × 7 × 8
Greek numeral ΣΠ´
Roman numeral CCLXXX
Binary 1000110002
Ternary 1011013
Quaternary 101204
Quinary 21105
Senary 11446
Octal 4308
Duodecimal 1B412
Vigesimal E020
Base 36 7S36

280 (two hundred [and] eighty) is the natural number after 279 and before 281.

## In mathematics

The denominator of the eighth harmonic number,[1] 280 is an octagonal number.[2]

There are 280 plane trees with ten nodes. As a consequence of this, 18 people around a round table can shake hands with each other in non-crossing ways, in 280 different ways (this includes rotations).[disputed ]

280 is a base 10 Harshad number.

## Integers from 281 to 289

### 281

281 = prime, twin prime with 283, Sophie Germain prime, sum of the first fourteen primes, sum of seven consecutive primes (29 + 31 + 37 + 41 + 43 + 47 + 53), Chen prime, Eisenstein prime with no imaginary part, centered decagonal number

### 282

282 = 2·3·47, sphenic number

### 283

283 prime, twin prime with 281, strictly non-palindromic number

### 284

284 = 22·71, amicable number with 220; nontotient. 284 degrees Celsius is the flash point of paper.

### 285

285 = 3·5·19, sphenic number, square pyramidal number, Harshad number, also in Star Trek, the total number of Rules of Acquisition, repdigit in base 7 (555).

### 286

286 = 2·11·13, sphenic number, tetrahedral number, nontotient, also shorthand for the Intel 80286 microprocessor chip

### 287

287 = 7·41, sum of three consecutive primes (89 + 97 + 101), sum of five consecutive primes (47 + 53 + 59 + 61 + 67), sum of nine consecutive primes (17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47), Kynea number, pentagonal number, also shorthand for the Intel math coprocessor to the 80286

### 288

288 = 25·32, is a pentagonal pyramidal number, is 4 superfactorial since 288 = 1!·2!·3!·4!, is an untouchable number, a Harshad number in base 10, a self number, is sum of the sequence of integers 1..4 to the second tetration since 288 = 1 + 4 + 27 + 256 = 11 + 22 + 33 + 44, the number of labelled pointed rooted trees (vertebrates) with up to 4 nodes, the number of maximal directed Pseudoforests on up to 4 vertices, the number of Endofunctions for all sets with <=4 points, and is two dozen sets of a dozen, thus being two gross, often told as a pun in maths classes

### 289

289 = 172, centered octagonal number, Friedman number since (8 + 9)^2 = 289.

## References

1. ^ "Sloane's A002805 : Denominators of harmonic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
2. ^ "Sloane's A000567 : Octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.