A236619 a(n) = |{0 < k < n: prime(m)^3 + 2*m^3 and m^3 + 2*prime(m)^3 are both prime with m = 3*phi(k) + phi(n-k) - 1}|, where phi(.) is Euler's totient function.
0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 2, 0, 0, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 2, 4, 0, 1, 3, 0, 2, 3, 3, 2, 3, 1, 3, 2, 3, 3, 2, 4, 3, 4, 2, 0, 2, 5, 4, 2, 4, 2, 2, 3, 5, 5, 6
Offset: 1
Keywords
Examples
a(51) = 1 since 3*phi(35) + phi(51-35) - 1 = 3*24 + 8 - 1 = 79 with prime(79)^3 + 2*79^3 = 401^3 + 2*79^3 = 65467279 and 79^3 + 2*prime(79)^3 = 79^3 + 2*401^3 = 129455441 both prime.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
p[n_]:=PrimeQ[Prime[n]^3+2*n^3]&&PrimeQ[n^3+2*Prime[n]^3] f[n_,k_]:=3*EulerPhi[k]+EulerPhi[n-k]-1 a[n_]:=Sum[If[p[f[n,k]],1,0],{k,1,n-1}] Table[a[n],{n,1,100}]
Comments