Thread: prime divisors
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Old 2021-06-14, 16:24   #4
MattcAnderson's Avatar
"Matthew Anderson"
Dec 2010
Oregon, USA

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

Originally Posted by MattcAnderson View Post
new observation about divisors and positive integers (whole numbers)

an curve fit with recursion namely

b(0)=2 for squares
b(0) = 3 for cubes


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,
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.
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