mersenneforum.org > Math Search for a number theoretic function related to "prime divisor sums"
 User Name Remember Me? Password
 Register FAQ Search Today's Posts Mark Forums Read

 2004-07-04, 09:31 #1 juergen   Mar 2004 29 Posts Search for a number theoretic function related to "prime divisor sums" Hi all, does anybody know a number theoretic function similar to the divisor sum, but which only sums up the divisors which are prime? For me a function would be interesting, which builds the 1. Sum over p/x for all primes p which divide x where p<>x or 2. Sum over p for all primes p which divide x where p<>x (the same as aove * x) Of course I could invent this function myself, but I hope that it already exists and maybe there are already some interestings fact known about this function which I could use :o) I am especially interested in Numbers x which have a Sum (1.) >= 1 in the function mentioned above (or 2. >= x). Does anybody know something about such functions or such numbers? Thank you in advance Juergen Last fiddled with by juergen on 2004-07-04 at 09:35 Reason: adding some more info
2004-07-06, 21:17   #2
juergen

Mar 2004

29 Posts

Quote:
 Originally Posted by juergen Hi all, does anybody know a number theoretic function similar to the divisor sum, but which only sums up the divisors which are prime? For me a function would be interesting, which builds the 1. Sum over p/x for all primes p which divide x where p<>x or 2. Sum over p for all primes p which divide x where p<>x (the same as aove * x) I am especially interested in Numbers x which have a Sum (1.) >= 1 in the function mentioned above (or 2. >= x). Does anybody know something about such functions or such numbers? Thank you in advance Juergen
Hi all,

sorry I missed something in the second form. It is wrong :o(
The first form is correct and the condition Sum (1.) >= 1.

I am trying to learn something about numbers x for which this sum is greather than x. One example is

30 <= 31

30=2*3*5
31=30/2 + 30/3 + 30/5 = 15 + 10 + 6

Does anybody know something about such numbers?

Thank you in advance

Juergen

 2004-07-10, 23:01 #3 juergen   Mar 2004 358 Posts Hi all, the sum over 1/p for all prime p < x is called the reciprocal prime sum. If you are interested you will find further info on mathworld by searching for "mertens constant". regards Juergen

 Similar Threads Thread Thread Starter Forum Replies Last Post a1call Miscellaneous Math 179 2015-11-12 14:59 Kosmaj Riesel Prime Search 21 2012-09-14 09:51 ewmayer Math 10 2007-03-02 12:47 rdotson Hardware 18 2005-09-25 13:04 nitai1999 Software 7 2004-08-26 18:12

All times are UTC. The time now is 03:03.

Sat Nov 28 03:03:49 UTC 2020 up 79 days, 14 mins, 3 users, load averages: 1.01, 1.12, 1.10