login
Numbers that can be written as the sum of two primes, p, q, where p < q such that q^2 - p^2 is squarefree.
0

%I #10 Jul 21 2019 13:25:26

%S 5,7,15,19,21,33,39,43,55,61,69,73,91,105,109,111,115,133,141,159,165,

%T 181,183,195,199,201,213,231,235,241,253,259,271,273,285,295,309,313,

%U 339,349,381,385,399,403,411,421,433,435,451,465,469,489,493,501,505

%N Numbers that can be written as the sum of two primes, p, q, where p < q such that q^2 - p^2 is squarefree.

%e 5 is in the sequence since 5 = 2 + 3 (both prime) and since 3^2 - 2^2 = 5 is squarefree.

%e 7 is in the sequence since 7 = 2 + 5 (both prime) and since 5^2 - 2^2 = 21 is squarefree.

%t Flatten[Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]) MoebiusMu[(n - i)^2 - i^2]^2, {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 500}]]

%Y Cf. A309277.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Jul 21 2019