146 (number)

146 magnetic balls, arranged to show that 146 is an octahedral number

← 145 146 147 →
← 140 141 142 143 144 145 146 147 148 149 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
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.

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

• 146 (disambiguation)

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.