96 (ninety-six) is the natural number following 95 and preceding 97. It is a number that appears the same when turned upside down.

In mathematics

thumb|200px|96 as the difference of two squares (in orange).

96 is:

  • an octagonal number.
  • a refactorable number.
  • an untouchable number.
  • a semiperfect number since it is a multiple of 6.
  • an abundant number since the sum of its proper divisors is greater than 96.
  • the fourth Granville number and the second non-perfect Granville number. The next Granville number is 126, the previous being 24.
  • the sum of Euler's totient function φ(x) over the first seventeen integers.
  • strobogrammatic in bases 10 (96<sub>10</sub>), 11 (88<sub>11</sub>) and 95 (11<sub>95</sub>).
  • palindromic in bases 11 (88<sub>11</sub>), 15 (66<sub>15</sub>), 23 (44<sub>23</sub>), 31 (33<sub>31</sub>), 47 (22<sub>47</sub>) and 95 (11<sub>95</sub>).
  • an Erdős–Woods number, since it is possible to find sequences of 96 consecutive integers such that each inner member shares a factor with either the first or the last member.
  • divisible by the number of prime numbers (24) below 96.
  • the smallest natural number that can be expressed as the difference of two nonzero squares in more than three ways: <math>10^2-2^2</math>, <math>11^2-5^2</math>, <math>14^2-10^2</math> or <math>25^2-23^2</math>.

The number of divisors of 96 is 12. As no smaller number has more than 12 divisors, 96 is a largely composite number.

Skilling's figure, a degenerate uniform polyhedron, has Euler characteristic <math>\chi=-96.</math>

Every integer greater than 96 may be represented as a sum of distinct super-prime numbers.

References

  • On the number 96