Number Factoids

Another break in the Thanksgiving cooking. Check out tingilinde: take a number …. I’m far from a mathematician (and was even when I dated one), but I find this list of number facts magical and opaque. These are my favorite of the inscrutable, OCD, and sometimes just silly observations:

• 4 is the smallest number of colors sufficient to color all planar maps.
• 11 is the largest known multiplicative persistence.
• 17 is the number of wallpaper groups.
• 36 is the smallest number (besides 1) which is both square and triangular.
• 38 is the last Roman numeral when written lexicographically.
• 92 is the number of different arrangements of 8 non-attacking queens on an 8x8 chessboard.
• 136 is the sum of the cubes of the digits of the sum of the cubes of its digits.
• 405 is a pentagonal pyramidal number.
• 570 is the product of all the prime palindromic Roman numerals.
• 1005 is the smallest number whose English name contains all five vowels exactly once.
• 1084 is the smallest number whose English name contains all five vowels in order.
• 1435 is a vampire number.
• 1650 has exactly the same digits in 3 different bases.
• 1666 is the sum of the Roman numerals.

Anyone know what a vampire number is? An amicable number? And can anyone help him fill in the ???'s? (Huh, looking at the list, I'm reminded that I kind of liked geometry.)