Misplaced Pages

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

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: ${\displaystyle 10^{2}-2^{2}}$, ${\displaystyle 11^{2}-5^{2}}$, ${\displaystyle 14^{2}-10^{2}}$ or ${\displaystyle 25^{2}-23^{2}}$.

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 a Euler characteristic ${\displaystyle \chi =-96.}$

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

References

1. "Sloane's A000567 : Octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
2. "Sloane's A033950: Refactorable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
3. "Sloane's A005114 : Untouchable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
4. "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
5. Sloane, N. J. A. (ed.). "Sequence A334078". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. Sloane, N. J. A. (ed.). "Sequence A000005 (d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
7. Sloane, N. J. A. (ed.). "Sequence A067128 (Ramanujan's largely composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

External links

• On the number 96

• Integers