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From Wikipedia, the free encyclopedia

240 (two hundred [and] forty) is the natural number following 239 and preceding 241.

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In mathematics

240 is:

  • a semiperfect number.[1]
  • a concatenation of two of its proper divisors.[2]
  • a highly composite number since it has 20 divisors total (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, and 240), more than any previous number.
  • a refactorable number or tau number, since it has 20 divisors and 20 divides 240.
  • a highly totient number, since it has 31 totient answers, more than any previous integer.
  • a pronic number since it can be expressed as the product of two consecutive integers, 15 and 16.
  • palindromic in bases 19 (CC19), 23 (AA23), 29 (8829), 39 (6639), 47 (5547) and 59 (4459).
  • a Harshad number in bases 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, 14, 15 (and 73 other bases).
  • the aliquot sum of 120 and 57121.
  • part of the 12161-aliquot tree. The aliquot sequence starting at 120 is: 120, 240, 504, 1056, 1968, 3240, 7650, 14112, 32571, 27333, 12161, 1, 0.

240 can be expressed as a sum of consecutive primes in two different ways: 240 = 53 + 59 + 61 + 67 = 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43.

E8 has 240 roots.

There are 240 distinct solutions of the Soma cube puzzle.[3]

In other fields

240 is:

References

  1. ^ "Sloane's A005835 : Pseudoperfect (or semiperfect) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-09-05.
  2. ^ "Sloane's A050480 : Numbers that can be written as a concatenation of distinct proper divisors". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-09-05.
  3. ^ Weisstein, Eric W. "Soma Cube". Wolfram MathWorld. Retrieved 2016-09-05.
This page was last edited on 12 February 2019, at 16:33
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