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146 (one hundred ndforty-six) is the
146 (one hundred ndforty-six) is the natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
following 145 and preceding 147 147 may refer to:
* 147 (number), a natural number
* AD 147, a year of the Julian calendar, in the second century
* 147 BC, a year of the pre-Julian Roman calendar
* 147 AH, a year in the Islamic calendar that corresponds to 764 – 765 CE
...
.
In mathematics
146 is anoctahedral number
In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres. The ''n''th octahedral number O_n can be obtained by the formula:.
:O_n=.
The first few octahed ...
, the number of spheres that can be packed into in a regular octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
with six spheres along each edge. For an octahedron with seven spheres along each edge, the number of spheres on the surface of the octahedron is again 146. It is also possible to arrange 146 disks in the plane into an irregular octagon with six disks on each side, making 146 an octo number.
There is no integer with exactly 146 coprime
In mathematics, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equivale ...
s less than it, so 146 is a nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotient ...
. It is also never the difference between an integer and the total of coprimes below it, so it is a noncototient In mathematics, a noncototient is a positive integer ''n'' that cannot be expressed as the difference between a positive integer ''m'' and the number of coprime integers below it. That is, ''m'' − φ(''m'') = ''n'', where Ï ...
. And it is not the sum of proper divisors of any number, making it an 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 (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. ...
.
There are 146 connected partially ordered set
In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a Set (mathematics), set. A poset consists of a set toget ...
s with four labeled elements.
See also
*146 (disambiguation) 146 may refer to:
*146 (number), a natural number
* AD 146, a year in the 2nd century AD
*146 BC, a year in the 2nd century BC
*146 (Antrim Artillery) Corps Engineer Regiment, Royal Engineers
See also
* List of highways numbered 146
The followin ...
References
{{Integers, 1 Integers