| 词条 | 280 (number) |
| 释义 |
| number = 280 }} 280 (two hundred [and] eighty) is the natural number after 279 and before 281. In mathematicsThe 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-inline|reason=This seems to be an error, the number of plane (rooted) trees with ten vertices and the number of handshakes (non-intersecting chords with 18 points around a circle) should both be the ninth Catalan number. OEIS http://oeis.org/A000108 for the Catalan numbers has both of these ideas listed, "Ways of joining 2n points on a circle to form n nonintersecting chords." so 18 points is ninth Catalan # and "a(n) is the number of ordered rooted trees with n nodes, not including the root." so again, 10 roots is Catalan (9). And this number is 4862, not 280.|date=September 2013}} 280 is a base 10 Harshad number. In geography
See also the year 280. Integers from 281 to 289281{{Main|281 (number)}}282282 = 2·3·47, sphenic number 283283 prime, twin prime with 281, strictly non-palindromic number 284{{Main|284 (number)}}285285 = 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). 286286 = 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). 287287 = 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{{Main|288 (number)}}289289 = 172, centered octagonal number, Friedman number since (8 + 9)^2 = 289. References1. ^{{Cite web|url=https://oeis.org/A002805|title=Sloane's A002805 : Denominators of harmonic numbers|last=|first=|date=|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}} {{Integers|2}}{{DEFAULTSORT:280 (Number)}}2. ^{{Cite web|url=https://oeis.org/A000567|title=Sloane's A000567 : Octagonal numbers|last=|first=|date=|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}} 1 : Integers |
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