280 (number)

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

This article covers the number 280. For the year, see 280.
← 279 280 281 →
Cardinaltwo hundred eighty
Ordinal280th
(two hundred eightieth)
Factorization23 × 5 × 7
Greek numeralΣΠ´
Roman numeralCCLXXX
Binary1000110002
Ternary1011013
Senary11446
Octal4308
Duodecimal1B412
Hexadecimal11816

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).

Integers from 281 to 289

281
Main article: 281 (number)

282

282 = 2·3·47, sphenic number, number of planar partitions of 9[3]

283

283 prime, twin prime with 281, strictly non-palindromic number, 4283 - 3283 is prime

284

284 and 220 form the first pair of amicable numbers, as the divisors of 284 add up to 220 and vice versa.[4]

285

285 = 3·5·19, sphenic number, square pyramidal number, Harshad number, repdigit in base 7 (555), vertically symmetric number (sequence A053701 in the OEIS).

286

286 = 2·11·13, sphenic number, tetrahedral number, nontotient.

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.

288
Main article: 288 (number)

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.
  3. Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.