96 (number)

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: 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.

References

References

1. "Sloane's A000567 : Octagonal numbers". OEIS Foundation.
2. "Sloane's A033950: Refactorable numbers". OEIS Foundation.
3. "Sloane's A005114 : Untouchable numbers". OEIS Foundation.
4. "Sloane's A059756 : Erdős-Woods numbers". OEIS Foundation.
5. {{cite OEIS. A334078
6. {{Cite OEIS. A000005. d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.
7. {{Cite OEIS. A067128. Ramanujan's largely composite numbers