280 (number)

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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] 280 is the smallest octagonal number that is a half of another octagonal number.

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 – discuss]}

280 is a base 10 Harshad number.

In geography[]

• List of highways numbered 280

See also the year 280.

Integers from 281 to 289[]

281[]

282[]

282 = 2·3·47, sphenic number

283[]

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

284[]

284 and 220 form the first pair of amicable numbers, as the divisors of 284 add up to 220 and vice versa.^[3]

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.

286 is the smallest even pseudoprime (not divisible by 3) to base 3, which implies 3²⁸⁵ ≡ 1 (mod 286).

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), pentagonal number, also shorthand for the Intel math coprocessor to the 80286

288[]

289[]

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

References[]