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(n1) + 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.