96 (number)

Template:Infobox number 96 (ninety-six) is the natural number following 95 and preceding 97. It is a number that appears the same when rotated by 180 degrees.

In mathematics

File:96-square-difference.png

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 (96₁₀), 11 (88₁₁) and 95 (11₉₅).
• palindromic in bases 11 (88₁₁), 15 (66₁₅), 23 (44₂₃), 31 (33₃₁), 47 (22₄₇) and 95 (11₉₅).
• 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: $10^2-2^2$, $11^2-5^2$, $14^2-10^2$ or $25^2-23^2$.

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 $\chi =-96.$

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

External links

• On the number 96