270 (number)

270 (two hundred [and] seventy) is the natural number following 269 and preceding 271.

← 269 270 271 →
Cardinaltwo hundred seventy
Ordinal270th
(two hundred seventieth)
Factorization2 × 33 × 5
Greek numeralΣΟ´
Roman numeralCCLXX
Binary1000011102
Ternary1010003
Senary11306
Octal4168
Duodecimal1A612
Hexadecimal10E16

In mathematics
  • 270 is a harmonic divisor number[1]
  • 270 is the fourth number that is divisible by its average integer divisor[2]
  • 270 is a practical number, by the second definition
  • The sum of the coprime counts for the first 29 integers is 270
  • 270 is a sparsely totient number, the largest integer with 72 as its totient
  • Given 6 elements, there are 270 square permutations[3]
  • 10! has 270 divisors
  • 270 is a Harshad number in base 10
  • 270 is the smallest positive integer that has divisors ending by digits 1, 2, ..., 9.
  • 270 is the smallest sum of a set of even numbers that contain every digit once.

Integers from 271 to 279

271
Main article: 271 (number)

272

272 = 24·17, sum of four consecutive primes (61 + 67 + 71 + 73), Euler number, primitive semiperfect number, pronic number. 272 is the smallest palindrome divisible by a fourth power.

273
Main article: 273 (number)

274

274 = 2·137, tribonacci number, Smith number, nontotient, noncototient, centered triangular number, 27464 + 1 is prime

275

275 = 52·11. 275 is the sum of fifth powers of the first two primes. The maximal number of pieces that can be obtained by cutting an annulus with 22 cuts.[4]

276
Main article: 276 (number)

277
Main article: 277 (number)

278

278 = 2·139 = Φ(30),[5] nontotient. 278 is the smallest semiprime such that the next semiprime (287) is its anagram.

279

279 = 32·31. Every positive integer is the sum of at most 279 eighth powers. See Waring's problem.

References
  1. Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  2. Sloane, N. J. A. (ed.). "Sequence A007340". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. Sloane, N. J. A. (ed.). "Sequence A003483". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. Sloane, N. J. A. (ed.). "Sequence A000096". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. Sloane, N. J. A. (ed.). "Sequence A002088". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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