146_(number)

146 (number)

146 (number)

Natural number

146 (one hundred [and] forty-six) is the natural number following 145 and preceding 147.

146 magnetic balls, arranged to show that 146 is an octahedral number
Quick Facts ← 145 146 147 →, Cardinal ...

In mathematics

146 is an octahedral number, the number of spheres that can be packed into in a regular octahedron with six spheres along each edge.[1] For an octahedron with seven spheres along each edge, the number of spheres on the surface of the octahedron is again 146.[2] 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.[3]

There is no integer with exactly 146 coprimes less than it, so 146 is a nontotient. It is also never the difference between an integer and the total of coprimes below it, so it is a noncototient.[4] And it is not the sum of proper divisors of any number, making it an untouchable number.[5]

There are 146 connected partially ordered sets with four labeled elements.[6]

See also

References

  1. [1]
    Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. [2]
    Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. [3]
    Sloane, N. J. A. (ed.). "Sequence A079273 (Octo numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. [4]
    Sloane, N. J. A. (ed.). "Sequence A058763 (Integers which are neither totient nor cototient)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. [5]
    Sloane, N. J. A. (ed.). "Sequence A005114 (Untouchable numbers, also called nonaliquot numbers: impossible values for the sum of aliquot parts function)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  6. [6]
    Sloane, N. J. A. (ed.). "Sequence A001927 (Number of connected partially ordered sets with n labeled points)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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