20210610, 22:32  #1 
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{4}·3·23 Posts 
prime divisors
Hi again all,
Some of us are familiar with proper divisors. For example, the proper divisors of 9 are 1 and 3. Also, the proper divisors of 35 are 5 and 7. ~ Made a Maple procedure called ProperDivisors(b). Has count function Pretty easy to understand For example  CPD(6) = 6 That is count proper divisors is 1 and two and three is 6. Another example CPD(19) = 1 See my 'blog o ria' My (big) question is, Suppose you have a general positive integer in factored form call it d. So d = p1^e1 * p2^e2 * ... what is its count of proper divisors? Is there a Maple function? what is CPD(d) ? Let me know. Regards, Matt 
20210614, 01:35  #2 
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{4}·3·23 Posts 
small insight
look
That took effort. Going to go eat now. Matt 
20210614, 06:39  #3 
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{4}·3·23 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(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 Last fiddled with by MattcAnderson on 20210614 at 07:45 Reason: another nifty file i typed 
20210614, 16:24  #4  
"Matthew Anderson"
Dec 2010
Oregon, USA
2^{4}×3×23 Posts 
singly recursive expression b(n) = 2*b(n1) + 1.
Quote:
Now I do a little Maple Code. I use notepad for the data tables and the insights. see attached. 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A way to search prime divisors of Mersenne numbers  Jinyuan Wang  Factoring  3  20200127 18:12 
Looking for fermat divisors, n=90120  firejuggler  Prime Sierpinski Project  2  20120110 17:14 
Sum of prime divisors for Mersenne Numbers?  kurtulmehtap  Math  3  20110119 18:48 
odd divisors of Mersennelike, question  stpascu  Factoring  1  20061016 16:31 
Number of divisors of n?  Citrix  Math  10  20060208 04:09 