Thread: prime divisors View Single Post
2021-06-14, 16:24   #4
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

24×32×7 Posts
singly recursive expression b(n) = 2*b(n-1) + 1.

Quote:
 Originally Posted by MattcAnderson new observation about divisors and positive integers (whole numbers) an curve fit with recursion namely b(0)=2 for squares or b(0) = 3 for cubes then b(n) = 2*b(n-1) + 1. This data table b Divisors(b) relevant expression 0 3 3^3 1 7 3^3*5 2 15 3^3*5*7 3 31 3^3*5*7*11 For example Divisors(3) could have relevant expression 7^3*23*29*17. We see that there is a prime squared followed by three distinct primes. Then Divisor(3) is 2*15 + 1 which is 31. Similarly, Divisors(2) could have relevant expression 17^3*3*5 and still Divisors(2) is still 15. So, in some sense, the primes are interchangable under this 'Divisors count' function. See you later, Matt
Today is a new day. I woke up, made my wife's cup, packed her lunch bag, and she is out the door.

Now I do a little Maple Code. I use notepad for the data tables and the insights.

see attached.
Attached Files
 proper divisors at one level recurrsin and a data table for Mersenne number.txt (432 Bytes, 41 views)