270 (number)

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Cardinaltwo hundred seventy
Ordinal270th
(two hundred seventieth)
Factorization2 × 33 × 5
Greek numeralΣΟ´
Roman numeralCCLXX
Binary1000011102
Ternary1010003
Octal4168
Duodecimal1A612

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.

Integers from 271 to 279

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.

275

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

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

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.