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
1D_{16} 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 
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