Sums of primes divisibility sequences
There are many sequences dealing with the sums of primes and their divisibility. They are summarized here.
The sum of the th power of the first n primes:
One plus the sum of the th power of the first n primes:
Column headings in the table below: a as defined above n div a n divides a p(a,n) pi(n) where n divides a b as defined above n div b n divides b p(b,n) pi(n) where n divides b sum(n div a) sum of the primes where n divides a avg(n div a) average of the primes where n divides a
NOGI Not of great interest
- Javier Cilleruelo and Florian Luca, On the sum of the first n primes, Q. J. Math. 59:4 (2008), 14 pp.
- Kaisa Matomäki, A note on the sum of the first n primes, Quart. J. Math. 61 (2010), pp. 109-115.
- The Prime Puzzles & Problems Connection: Puzzle 31.- The Average Prime number, APN(k) = S(Pk)/k.
- Eric Weisstein's World of Mathematics, Prime Sums