Thread: prime divisors
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Old 2021-06-14, 06:39   #3
MattcAnderson
 
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"Matthew Anderson"
Dec 2010
Oregon, USA

11100010102 Posts
Thumbs up 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
File Type: txt more divisor count observation.txt (849 Bytes, 29 views)
File Type: txt 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
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