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22

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Please do not rely on any information it contains.            


22 is an integer.

Membership in core sequences

Even numbers ..., 14, 16, 18, 20, 22, 24, 26, 28, 30, ... A005843(11)
Composite numbers ..., 18, 20, 21, 22, 24, 25, 26, 27, 28, ... A002808
Semiprimes ..., 14 15, 21, 22, 25, 26, 33, 34, 35, ... A001358
Squarefree numbers ..., 17, 19, 21, 22, 23, 26, 29, 30, 31, ... A005117
Pentagonal numbers 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ... A000326

In Pascal's triangle, 22 occurs twice.

Sequences pertaining to 22

Multiples of 22 0, 22, 44, 66, 88, 110, 132, 154, 176, 198, ... A005843
22-gonal numbers 0, 1, 22, 63, 124, 205, 306, 427, 568, 729, ... A051874
Centered 22-gonal numbers 1, 23, 67, 133, 221, 331, 463, 617, 793, ... A069173
Concentric 22-gonal numbers 1, 22, 45, 88, 133, 198, 265, 352, 441, 550, ... A195149
sequence beginning at 9 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, ... A033479

Partitions of 22

There are 1002 partitions of 22.

The Goldbach representations of 22 are: 3 + 19 = 5 + 17 = 11 + 11.

Roots and powers of 22

In the table below, irrational numbers are given truncated to eight decimal places.

4.69041575 A010478 22 2 484
2.80203933 A010594 22 3 10648
2.16573677 A011018 22 4 234256
1.85560073 A011107 22 5 5153632
1.67392930 22 6 113379904
1.55515853 22 7 2494357888
1.47164424 22 8 54875873536
1.40980184 22 9 1207269217792
1.36220436 22 10 26559922791424
A009966

Logarithms and 22nd powers

In the OEIS specifically and mathematics in general, log x refers to the natural logarithm of x, whereas all other bases are specified with a subscript.

As above, irrational numbers in the following table are truncated to eight decimal places.

TABLE

Values for number theoretic functions with 22 as an argument

1
–3
8
36
4
10
2
2
10 This is the Carmichael lambda function.
1 This is the Liouville lambda function.
1.00000023845... (see A013668).
22! 1124000727777607680000
51090942171709440000

Factorization of some small integers in a quadratic integer ring adjoining the square roots of −22, 22

The commutative quadratic integer ring with unity , with units of the form (), is a unique factorization domain.

2 Irreducible
3 Prime
4 2 2
5 Prime
6 2 × 3
7 Prime
8 2 3
9 3 2
10 2 × 5
11 Irreducible
12 2 2 × 3
13 Irreducible
14 2 × 7
15 3 × 5
16 2 4
17 Prime
18 2 × 3 2
19 Irreducible Prime
20 2 2 × 5
21 3 × 7
22 2 × 11 OR
23 Prime
24
25
26 2 × 13 OR
27
28
29
30

It almost goes without saying that is not a distinct factorization of 22, since this is a UFD and we readily see that .

Ideals help us make sense of multiple distinct factorizations.

Factorization of
In In
2
3 Prime
5 Prime
7
11
13
17 Prime Prime
19
23
29
31
37
41
43
47

Factorization of 22 in some quadratic integer rings

Of course 22 is composite in all quadratic integer rings. However, in some, one of its two prime factors (2 or 11) is further reducible, and in some, both prime factors are further reducible.

2 × 11
2 × 11
2 × 11 2 × 11

Representation of 22 in various bases

Base 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Representation 10110 211 112 42 34 31 26 24 22 20 1A 19 18 17 16 15 14 13 12

Although 22 is a palindromic number in base 10, note that that is the only base that, in the range from 2 to 20, it is palindromic in (it is trivially palindromic in base 21 and all bases higher than 22).

See also

Some integers
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
1729