This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Lixin Zheng has authored 3 sequences.
660 has prime divisors 2,3,5,11.
|PSL_2(11)| = 660 = 2^2 * 3 * 5 * 11.
is:=function(n) return IsPrimePowerInt(n) and Length(Unique(FactorsInt(n*(n^2-1))))=4; end; Filtered([2..1000], n -> is(n)); # Charles R Greathouse IV, Jul 03 2023; edited by Lixin Zheng, Jun 23 2024
is(n)=isprimepower(n) && omega(lcm([n-1,n,n+1]))==4 \\ Charles R Greathouse IV, Jul 03 2023
H(n)=isprimepower(n/2^valuation(n,2)/3^valuation(n,3)) list(lim)=my(v=List(), N); lim\=1; for(n=1, logint(lim\2+1, 3), N=2*3^n; while(N<=lim+1, if(isprimepower(N-1) && H(N-2), listput(v, N-1)); if(isprimepower(N+1) && H(N+2) && N+1<=lim, listput(v, N+1)); N<<=1)); for(n=4,logint(N+1,2), N=2^n; if(H(N-1) && H(N+1) && N<=lim, listput(v,N)); if(isprimepower(N-1) && H(N-2), listput(v,N-1)); if(isprimepower(N+1) && H(N+2) && N+1<=lim, listput(v,N+1))); for(n=3,logint(N,3), N=3^n; if(H(N-1) && H(N+1), listput(v,N))); Set(v) \\ Charles R Greathouse IV, Jul 03 2023
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.
# 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())
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
Comments