96 (number)

96 is:

• an octagonal number.^[1]
• a refactorable number.^[2]
• an untouchable number.^[3]
• 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.^[4]
• 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: ${\displaystyle 10^{2}-2^{2}}$, ${\displaystyle 11^{2}-5^{2}}$, ${\displaystyle 14^{2}-10^{2}}$ or ${\displaystyle 25^{2}-23^{2}}$.^[5]

The number of divisors of 96 is 12.^[6] As no smaller number has more than 12 divisors, 96 is a largely composite number.^[7]

Skilling's figure, a degenerate uniform polyhedron, has Euler characteristic ${\displaystyle \chi =-96.}$

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