20040704, 09:31  #1 
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 20040704 at 09:35 Reason: adding some more info 
20040706, 21:17  #2  
Mar 2004
29 Posts 
Quote:
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 

20040710, 23:01  #3 
Mar 2004
35_{8} 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 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
The "one billion minus 999,994,000" digits prime number  a1call  Miscellaneous Math  179  20151112 14:59 
Welcome to "Riesel Prime Search"  Kosmaj  Riesel Prime Search  21  20120914 09:51 
PrimeRelated History: Leibniz' "Universal Language Based on Primes"  ewmayer  Math  10  20070302 12:47 
Numbertheoretic FPGA function implementation suggestions?  rdotson  Hardware  18  20050925 13:04 
Would Minimizing "iterations between results file" may reveal "is not prime" earlier?  nitai1999  Software  7  20040826 18:12 