odditudes-and-weirdities

Happy World Goat Day! This is another holiday where the webpage I used to use for it disappeared so I'm writing one to replace it. As is often the case I don't know why today was selected for World Goat Day. As a species that was domesticated back in prehistoric times, today's date is unlikely to denote some milestone in human-goat relations. Regardless of why today's date is World Goat Day, goats have been important livestock for an estimated 10,000 years. But I don't think today is supposed to be about the domesticated goat in particular; since the original webpage I had for it was for a zoo, I suspect today is about celebrating all the animals in the goat genus . This includes guys like the Markhor (the world's largest goat), various ibexes like the Alpine Ibex , domesticated goats, et al. (Sorry Mountain Goat , but unfortunately you're not considered to be a true goat, though clearly a goat relative.) Further up the taxonomy hierarchy, goats are in the...

Happy Almost Perfect Numbers Day! Today we celebrate numbers that aren't perfect numbers but are almost perfect numbers  (aka slightly deficient numbers aka least defective numbers). Perfect numbers (in case you've forgotten) are the numbers such that if you sum up their divisors the result is 2 times the number itself. For example, the divisors of 6 are 1, 2, 3, and 6, and if you sum them up you get 1+2+3+6=12, which is also 2 x 6. Almost perfect numbers are numbers where the sum of the divisors is 1 less than 2 times the number. For example, the divisors of 4 are 1, 2, and 4, and the sum of them is 1+2+4 = 7, which is 1 less than 2 x 4. All the known almost perfect numbers are powers of 2, like 2x2 = 4, 2x2x2 = 8, 2x2x2x2 = 16, etc. It hasn't been proven that every almost perfect number is of this form, though given the computational power we have today, if other forms exist, they must be very large almost perfect numbers. Here is the beginning of the almost perfect numb...