270 (number)

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

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.

In other fields[]

• The year 270 BC
• The year 270 AD
• The caliber of the .270 Winchester rifle
• The number of U.S. Electoral College votes needed to be elected President of the United States
• The average number of days in human pregnancy

Integers from 271 to 279[]

271[]

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[]

274[]

274 = 2·137, tribonacci number, Smith number, nontotient, noncototient, centered triangular number

275[]

275 = 5²·11. 275 is the sum of fifth powers of the first two primes.

276[]

277[]

278[]

278 = 2·139, 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[]