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162 (number)

From Wikipedia, the free encyclopedia
Natural number
← 161162 163 →
Cardinalone hundred sixty-two
Ordinal162nd
(one hundred sixty-second)
Factorization2 × 34
Divisors1, 2, 3, 6, 9, 18, 27, 54, 81, 162
Greek numeralΡΞΒ´
Roman numeralCLXII,clxii
Binary101000102
Ternary200003
Senary4306
Octal2428
Duodecimal11612
HexadecimalA216

162 (one hundred [and] sixty-two) is thenatural number between161 and163.

In mathematics

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Having only 2 and 3 as its prime divisors, 162 is a3-smooth number.[1] 162 is also anabundant number, since its sum of divisors1+2+3+6+9+18+27+54+81=201{\displaystyle 1+2+3+6+9+18+27+54+81=201} is greater than it.[2] As the product3×6×9=162{\displaystyle 3\times 6\times 9=162} of numbers three units apart from each other, it is a triple factorial number.[3]

There are 162 ways of partitioning seven items into subsets of at least two items per subset.[4]16264 + 1 is a prime number.

References

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  1. ^Sloane, N. J. A. (ed.)."Sequence A003586 (3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation..
  2. ^Sloane, N. J. A. (ed.)."Sequence A005101 (Abundant numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^Sloane, N. J. A. (ed.)."Sequence A007661 (Triple factorial numbers)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^Sloane, N. J. A. (ed.)."Sequence A000296 (Set partitions without singletons)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation.
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