This site is supported by donations to The OEIS Foundation.

# 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 $i\,$ th power of the first n primes: $a=\sum _{k=1}^{n}p_{k}^{i}\,$ One plus the sum of the $i\,$ th power of the first n primes: $b=1+\sum _{k=1}^{n}p_{k}^{i}\,$ ## Related Sequences

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



Sequences
i a n div a p(a,n) n div b p(b,n) sum(n div a) avg(n div a)
1 A007504 A045345 A171399 A128165 A233523 A050247 A050248
2 A024450 A111441 A217599 A128166 A233862 A217600 A217601
3 A098999 A122140 A223936 A128167 A233863 A223937 A223939
4 A122102 A125907 A232869 A128168 A233893
5 A122103 A122142 A224083 A128169 A234003 A224084 A224087
6 A236182 A125825 A232733 A128170 A233041 NOGI NOGI
7 A236209 A125826 A232865 A128171 A233040 NOGI NOGI
8 A236214 A125828 A232822 A232823 A232824 NOGI NOGI
9 A236215 A131263 A232962 A232964 A233042 NOGI NOGI
10 A236216 A131264 A233132 A233133 A233134 NOGI NOGI
11 A234740 A125827 A233192 A233193 A233194 NOGI NOGI
12 A236218 A131272 A233263 A233264 A233265 NOGI NOGI
13 A236221 A131273 A232770 A233349 A233350 NOGI NOGI
14 A236222 A131274 A232963 A232966 A233043 NOGI NOGI
15 A236223 A131275 A232848 A233413 A233414 NOGI NOGI
16 A236224 A131276 A233460 A233461 A233462 NOGI NOGI
17 A236225 A131277 A233555 A233556 A233557 NOGI NOGI
18 A236226 A131278 A233575 A233576 A233577 NOGI NOGI
19 A236227 A131279 A233767 A233768 A233769 NOGI NOGI