:96 (number)

File:96-square-difference.png

96 is:

• an octagonal number.{{Cite web|url=https://oeis.org/A000567|title=Sloane's A000567 : Octagonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}
• a refactorable number.{{Cite web|url=https://oeis.org/A033950|title=Sloane's A033950: Refactorable numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}
• an untouchable number.{{Cite web|url=https://oeis.org/A005114|title=Sloane's A005114 : Untouchable numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}
• 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.{{Cite web|url=https://oeis.org/A059756|title=Sloane's A059756 : Erdős-Woods numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-28}}
• 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 $25^2-23^2$.{{cite OEIS|A334078}}

The number of divisors of 96 is 12.{{Cite OEIS|A000005|d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.}} As no smaller number has more than 12 divisors, 96 is a largely composite number.{{Cite OEIS|A067128|Ramanujan's largely composite numbers}}

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

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

{{Reflist}}

• [http://www.wisdomportal.com/Numbers/96.html On the number 96]

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{{Integers|zero}}

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Category:Integers