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 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

2910 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?

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

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