- **MattcAnderson**
(*https://www.mersenneforum.org/forumdisplay.php?f=146*)

- - **prime divisors**
(*https://www.mersenneforum.org/showthread.php?t=26893*)

prime divisorsHi 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 |

small insight1 Attachment(s)
look
That took effort. Going to go eat now. Matt |

interesting to me2 Attachment(s)
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 |

singly recursive expression b(n) = 2*b(n-1) + 1.1 Attachment(s)
[QUOTE=MattcAnderson;580922]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[/QUOTE] 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. |

All times are UTC. The time now is 02:53. |

Powered by vBulletin® Version 3.8.11

Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.