146 (number)

146 magnetic balls, arranged to show that 146 is an octahedral number
← 145 146 147 →
Cardinalone hundred forty-six
Ordinal146th
(one hundred forty-sixth)
Factorization2 × 73
Divisors1, 2, 73, 146
Greek numeralΡΜϚ´
Roman numeralCXLVI
Binary100100102
Ternary121023
Senary4026
Octal2228
Duodecimal10212
Hexadecimal9216

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

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. ^ Sloane, N. J. A. (ed.). "Sequence A005900 (Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  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. ^ Sloane, N. J. A. (ed.). "Sequence A079273 (Octo numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  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. ^ 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. ^ 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.