In Mathematics
Twenty-two is an even composite number, its proper divisors being 1, 2 and 11. 22 is the sixth discrete semiprime and the fourth in the (2.q) family. With 21 it forms the second discrete semiprime pair. 22 has an aliquot sum of 14 and is the fifth composite number found in the 7-aliquot tree. It has a 7- member aliquot sequence 22, 14, 10, 8, 7, 1, 0 of which the next two members are themselves discrete semiprimes, 22 is the first discrete semiprime exhibiting this property. 169 also has 14 as its aliquot sum. 22 is itself the aliquot sum of two numbers 20, 38.
Twenty-two is a pentagonal number and a centered heptagonal number. When cutting a circle with just six line segments, the maximum number of pieces that can be so created is 22, thus 22 is a central polygonal number (see lazy caterer's sequence).
The sum of the totient function for the first eight integers is 22. 22 is a Perrin number, preceded in the sequence by 10, 12, 17.
22 divided by 7 approximates the irrational number π, the ratio of the circumference of a circle to its diameter.
Since it is possible to find sequences of 22 consecutive integers such that each inner member shares a factor with either the first or the last member, 22 is an Erdős–Woods number.
It is a Smith number in base 10.
Read more about this topic: 22 (number)
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