In Mathematics
Ten is a composite number, its proper divisors being 1, 2 and 5. Ten is the smallest noncototient, a number that cannot be expressed as the difference between any integer and the total number of coprimes below it.
Ten is the second discrete semiprime (2.5) and the second member of the (2.q) discrete semiprime family. Ten has an aliquot sum σ(n) of 8 and is accordingly the first discrete semiprime to be in deficit. All subsequent discrete semiprimes are in deficit. The aliquot sequence for 10 comprises five members (10,8,7,1,0) with this number being the second composite member of the 7-aliquot tree.
It is the aliquot sum of only one number the discrete semiprime 14.
Ten is a semi-meandric number.
Ten is the sum of the first three prime numbers, of the four first numbers (1 + 2 + 3 + 4), of the square of the two first odd numbers and also of the first four factorials (0! + 1! + 2! + 3!). Ten is the eighth Perrin number, preceded in the sequence by 5, 5, 7.
A polygon with ten sides is a decagon, and 10 is a decagonal number. But it is also a triangular number and a centered triangular number.
Ten is the number of n-Queens Problem solutions for n = 5.
Ten is the smallest number whose status as a possible friendly number is unknown.
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