12

Dear 12,

Hi! I hope everything is going okay for you. I'm a little worried because I see you everywhere and yet my daughter doesn't. Are you hiding from her? She loves to count, but after 11 she jumps right to 13. You are such a beautiful number I would really like her to get to know you. You are a dozen.

And thanks to Wikipedia I know this about you:

You are a composite number, the smallest number with exactly six divisors, your proper divisors being 1, 2, 3, 4 and 6. You arealso a highly composite number, the next one being 24.

You are composite number of the form p2q; a square prime, and also the first member of the (p2) family in this form.

You have an aliquot sum of 16 (133% in abundance). Accordingly, You are the first abundant number and demonstrates an 8 member aliquot sequence; {12,16,15,9,4,3,1,0} 12 is the 3rd composite number in the 3-aliquot tree. The only number which has 12 as its aliquot sum is the square 121. Only 2 other square primes are abundant (18 and 20).

The duodecimal system (1210 [twelve] = 1012), which is the use of 12 as a division factor for many ancient and medieval weights and measures, including hours, probably originates from Mesopotamia.

You are a superfactorial, being the product of the first three factorials.

You, being the product of three and four, the first four positive integers show up in the equation 12 = 3 × 4, which can be continued with the equation 56 = 7 × 8.

A twelve-sided polygon is a dodecagon. A twelve-faced polyhedron is a dodecahedron.

You are a pentagonal number.

The densest three-dimensional lattice sphere packing has each sphere touching 12 others, and this is almost certainly true for any arrangement of spheres (the Kepler conjecture). You are also the kissing number in three dimensions.

You are a number ada is that so coolio m*In base thirteen and higher bases (such as hexadecimal), you are represented as C.

You are superabundant, sparsely totient, a Harshad number and a Pell number.

You are the ninth Perrin number, preceded in the sequence by 5, 7, 10.

Twelve is the smallest weight for which a cusp form exists. This cusp form is the discriminant Δ(q) whose Fourier coefficients are given by the Ramanujan τ-function and which is (up to a constant multiplier) the 24th power of the Dedekind eta function. This fact is related to a constellation of interesting appearances of the number twelve in mathematics ranging from the value of the Riemann zeta function function at -1 i.e. ζ(-1)=-1/12, the fact that the abelianization of SL(2,Z) has twelve elements, and even the properties of lattice polygons.

You are a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number. Since there is a subset of 12's proper divisors that add up to 12 (all of them but with 4 excluded), YOU ARE a semiperfect number.

If an odd perfect number is of the form 12k+1, it has at least twelve distinct prime factors.

How cool are you? So please come out and play with my girl...

Best,
Kiki