OFFSET
1,7
COMMENTS
For integer n, this is the number of distinct pairs of primes p,q such that p+q <= n.
It appears that n = 30,31 are the only cases of a(n) = n.
LINKS
J. S. Williams, Prime graph components of finite groups, Journal of Algebra, 69(1981), 487-513.
EXAMPLE
For n = 5, the primes dividing the order of S_5 are 2,3,5. There is an element of order 6 in S_5, so there is an edge between 2 and 3, and there are no other edges. So a(5) = 1.
PROG
(Python) # Inefficient but works
import sympy
m = 100
dict1 = {}
for n in range(1, m):
edges = 0
for i in sympy.primerange(n):
for j in sympy.primerange(n):
if i != j and i + j <= n:
edges += 1
dict1[n] = int(edges/2)
print(dict1.values())
(Python)
from sympy import primepi, nextprime
def A363694(n):
c, m, p = 0, 1, 2
while p<<1 < n:
c += primepi(n-p)-m
p = nextprime(p)
m += 1
return c # Chai Wah Wu, Aug 05 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Lixin Zheng, Jun 15 2023
STATUS
approved