Answer: a) 496, yes
b) 8128, yes
496 = 16 31 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
8128 = 64 127 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064
284 = 22711, thus
1 + 2 + 4 + 71 + 142 = 220.
The number of factors is 6. 6 = 32
(Again, the pi product of one more than each exponent.)
284 is called a deficient number.
The sum of the divisors is less than itself.
220 and 284 are called amicable numbers
(meaning friendly number) and are the smallest pair.
Starting with 12496, you can form a longer chain of
sociable numbers.
BACK to the LESSON | ACTIVITY | NEXT LESSON |