146 (number)

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146 magnetic balls, arranged to show that 146 is an octahedral number Octahedral number.jpg
146 magnetic balls, arranged to show that 146 is an octahedral number
← 145 146 147 →
Cardinal one hundred forty-six
Ordinal 146th
(one hundred forty-sixth)
Factorization 2 × 73
Divisors 1, 2, 73, 146
Greek numeral ΡΜϚ´
Roman numeral CXLVI, cxlvi
Binary 100100102
Ternary 121023
Senary 4026
Octal 2228
Duodecimal 10212
Hexadecimal 9216

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

Contents

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] 146 is also a repdigit in base 8 (222).

See also

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA005900(Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA005899(Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA079273(Octo numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA058763(Integers which are neither totient nor cototient)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA005114(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.). "SequenceA001927(Number of connected partially ordered sets with n labeled points)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.