From Wikipedia, the free encyclopedia
Natural number
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Cardinal | one hundred thirty-two |
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Ordinal | 132nd (one hundred thirty-second) |
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Factorization | 22 × 3 × 11 |
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Divisors | 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132 |
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Greek numeral | ΡΛΒ´ |
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Roman numeral | CXXXII |
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Binary | 100001002 |
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Ternary | 112203 |
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Senary | 3406 |
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Octal | 2048 |
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Duodecimal | B012 |
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Hexadecimal | 8416 |
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132 (one hundred [and] thirty-two) is the
natural number following
131 and preceding
133.
In mathematics
132 is the sixth
Catalan number.
[1] With twelve divisors total where 12 is one of them, 132 is the 20th
refactorable number, preceding the
triangular
136.
[2]
132 is an
oblong number, as the product of 11 and 12
[3] whose sum instead yields the 9th
prime number
23;
[4] on the other hand, 132 is the 99th
composite number.
[5]
Adding all two-
digit
permutation subsets of 132 yields the same number:
- .
132 is the smallest number in
decimal with this property,
[6] which is shared by
264, 396 and 35964 (see
digit-reassembly number).
[7]
The number of
irreducible trees with fifteen
vertices is 132.
[8]
In a
toroidal board in the
n–Queens problem, 132 is the
count of non-attacking queens,
[9] with respective
indicator of
19
[10] and
multiplicity of
1444 =
382
[11] (where, 2 × 19 = 38).
[12]
The exceptional
outer automorphism of
symmetric group S6 uniquely maps vertices to factorizations and
edges to partitions in the
graph factors of the
complete graph with six vertices (and fifteen edges) K6, which yields 132
blocks in
Steiner system S(5,6,12).
In other fields
132 is also:
See also
References
-
^
"Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
-
^
Sloane, N. J. A. (ed.).
"Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-12.
-
^
Sloane, N. J. A. (ed.).
"Sequence A002378 (Oblong (or promic, pronic, or heteromecic) numbers: a(n) equal to n*(n+1).)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-12.
-
^
Sloane, N. J. A. (ed.).
"Sequence A000040 (The prime numbers.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-12.
-
^
Sloane, N. J. A. (ed.).
"Sequence A002808 (The composite numbers.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-12.
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^ Wells, D.
The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 138
-
^
Sloane, N. J. A. (ed.).
"Sequence A241754 (Numbers n equal to the sum of all numbers created from permutations of d digits sampled from n)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
-
^
Sloane, N. J. A. (ed.).
"Sequence A000014 (Number of series-reduced trees with n nodes.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-09-02.
-
^
Sloane, N. J. A. (ed.).
"Sequence A054502 (Counting sequence for classification of nonattacking queens on n X n toroidal board.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-10.
-
^
Sloane, N. J. A. (ed.).
"Sequence A054500 (Indicator sequence for classification of nonattacking queens on n X n toroidal board.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-10.
-
^
Sloane, N. J. A. (ed.).
"Sequence A054501 (Multiplicity sequence for classification of nonattacking queens on n X n toroidal board.)". The
On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-02-10.
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^ I. Rivin, I. Vardi and P. Zimmermann (1994).
The n-queens problem.
American Mathematical Monthly. Washington, D.C.:
Mathematical Association of America. 101 (7): 629–639.
doi:
10.1080/00029890.1994.11997004
JSTOR
2974691
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100,000
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1,000,000
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10,000,000
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100,000,000
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1,000,000,000
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