Fifty or Fifteen? Confusing Numbers
15 (fifteen) is the natural number following 14 and preceding 16. In English, it is the smallest natural number with seven letters in its spelled name.
In speech, the numbers 15 and 50 are often confused. When carefully enunciated, they differ in which syllable is stressed: 15 /fɪfˈtiːn/ vs 50 /ˈfɪfti/. However, in dates such as 1500 ("fifteen hundred") or when contrasting numbers in the teens, the stress generally shifts to the first syllable: 15 /ˈfɪftiːn/.
Fifteen is a triangular number, a hexagonal number, a pentatope number and the 5th Bell number (i.e. the number of partitions for a set of size 4). Fifteen is the double factorial of 5, and there are 15 perfect matchings of the complete graph K6 and 15 rooted binary trees with four labeled leaves, both of these being among the types of object counted by the double factorials. It is a composite number; its proper divisors being 1, 3 and 5. With only two exceptions, all prime quadruplets enclose a multiple of 15, with 15 itself being enclosed by the quadruplet (11, 13, 17, 19). 15 is also the number of supersingular primes.
The 15 perfect matchings of K6
15 is the 4th discrete semiprime (3.5) and the first member of the (3.q) discrete semiprime family. It is thus the first odd discrete semiprime. The number proceeding 15; 14 is itself a discrete semiprime and this is the first such pair of discrete semiprimes. The next example is the pair commencing 21.
The aliquot sum of 15 is 9, a square prime 15 has an aliquot sequence of 6 members (15,9,4,3,1,0). 15 is the fourth composite number in the 3-aliquot tree. The abundant 12 is also a member of this tree. Fifteen is the aliquot sum of the consecutive 4-power 16, and the discrete semiprime 33.
15 and 16 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.
