Thread: prime divisors View Single Post 2021-06-14, 06:39   #3
MattcAnderson

"Matthew Anderson"
Dec 2010
Oregon, USA

11100010102 Posts interesting to me

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
Attached Files more divisor count observation.txt (849 Bytes, 29 views) Anderson conjecture on divisors.txt (2.2 KB, 33 views)

Last fiddled with by MattcAnderson on 2021-06-14 at 07:45 Reason: another nifty file i typed  