96 (number)
Encyclopedia
96 is the natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

 following 95
95 (number)
95 is the natural number following 94 and preceding 96.-In mathematics:Ninety-five is the thirtieth distinct semiprime and the fifth of the form...

 and preceding 97
97 (number)
97 is the natural number following 96 and preceding 98.-In mathematics:97 is the 25th prime number , following 89 and preceding 101. 97 is a Proth prime as it is 3 × 25 + 1.The numbers 97, 907, 9007, 90007 and 900007 are happy primes...

.

In mathematics

Ninety-six is an octagonal number, a refactorable number
Refactorable number
A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that \tau|n. The first few refactorable numbers are listed in 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96...

 and an untouchable number
Untouchable number
An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer ....

. Since it is a multiple of 6, it is a semiperfect number
Semiperfect number
In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number....



Ninety-six is the fourth Granville number and the second non-perfect Granville number. The next Granville number is 126
126 (number)
126 is the natural number following 125 and preceding 127.-In mathematics:One hundred [and] twenty-six is a pentagonal pyramidal number, and a decagonal number as well as a pentatope number....

, the previous being 24
24 (number)
24 is the natural number following 23 and preceding 25.The SI prefix for 1024 is yotta , and for 10−24 yocto...

.

The sum of Euler's totient function
Euler's totient function
In number theory, the totient \varphi of a positive integer n is defined to be the number of positive integers less than or equal to n that are coprime to n In number theory, the totient \varphi(n) of a positive integer n is defined to be the number of positive integers less than or equal to n that...

 φ(x) over the first seventeen integers is 96.

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, 96 is an Erdős–Woods number
Erdos–Woods number
In number theory, an Erdős–Woods number is a positive integer that has the following property:Consider a sequence of consecutive positive integers [a, a+1, \dots, a+k]. The number k is an Erdős–Woods number if there exists such a sequence, beginning with some number a, in which each of the elements...

.

Every integer greater than 96 may be represented as a sum of distinct super-prime
Super-prime
Super-prime numbers are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence beginsThat is, if p denotes the ith prime number, the numbers in this sequence are those of the form p...

numbers.

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