16

You may know 16 simply as the number after 15 and before 17.

You’ll probably also recognise it as the square of 4.

Apparently, 16 is also the smallest number with exactly five divisors.

You may not know that:

  • As a power of 2 it has an aliquot sum one less than itself; 15, and is the fifth composite member of the 3-aliquot tree having the 7 member aliquot sequence (16, 15, 9, 4, 3, 1, 0).
  • Sixteen is the first number to be the aliquot sum of a lesser number; 12, it is also the aliquot sum of the greater number; the discrete semiprime, 26. It is the fourth power of two.
  • Sixteen is the only integer that equals mn and nm, for some unequal integers m and n (m = 4, n = 2, or vice versa). It has this property because 22 = 2 × 2. It is also equal to 32 (see tetration).
  • 15 and 16 form a Ruth–Aaron pair under the second definition in which repeated prime factors are counted as often as they occur.
  • Since it is possible to find sequences of 16 consecutive integers such that each inner member shares a factor with either the first or the last member, 16 is an Erd?s–Woods number. The smallest such range of 16 consecutive integers is from 2184 to 2200.
  • In bases 20, 24 and 30, sixteen is a 1-automorphic number (displayed as the numeral ‘G’).
  • 16 is a centered pentagonal number.
  • 16 is the base of the hexadecimal number system, which is used extensively in computer science.
  • 16 appears in the Padovan sequence, preceded by the terms 7, 9, 12 (it is the sum of the first two of these).

(isn’t wikipedia wonderful)

There was a time I used to know a bit about maths. But aliquot sums, composite numbers, discrete semiprimes, tetration, Ruth-Aaron pairs, consecutive integers, and the Padovan sequence mean nothing to me.

There was a time I didn’t know what it meant to be in love. But all that changed 16 years ago today. So that’s what 16 means to me. 16 years of being in love with, and being loved by the most beautiful girl I’ve ever known.

And I’ll take that over all the consecutive integers in the world.

Happy anniversary J. I love you and can’t think of anyone I’d rather spend an automorphic number of years with.