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:
i the power, primes are raised a as defined above n div a n divides a where n is not divisible by when n is a term, n is not divisible by any number of the set 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
There are no divisibility restrictions known for "n div b". Karl-Heinz Hofmann Mar 11 2021.
- 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