
Originally Posted by
Devils Horse
Curious about 48 too. Come on PL, have mercy on us pore ole redneck hillbillies and lay it on us. Maybe I could parlay your wisdom into enough bar bets to buy me some shoes and dentures.
Does the answer lie below?:
Forty-eight is a double factorial of 6, a highly composite number. Like all other multiples of 6, it is a semiperfect number. 48 is the second 17-gonal number.
48 is the first number of the form (24.q) and is in abundance having an aliquot sum of 76. It is the lowest composite number to fall into the 41-aliquot tree having the 7 aliquot number sequence,(48, 76 , 64, 63, 41, 1, 0). 48 is highly abundant with an aliquot sum 158% higher than itself.
48 is the smallest number with exactly ten divisors.
There are 11 solutions to the equation φ(x) = 48, namely 65, 104, 105, 112, 130, 140, 144, 156, 168, 180 and 210. This is more than any integer below 48, making 48 a highly totient number.
48 is in base 10 a Harshad number. It has 24, 2, 12,and 4 as factors.