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Sums of two primes whose difference is squarefree.
1

%I #8 Apr 20 2020 18:38:10

%S 5,7,8,9,12,15,16,19,20,21,24,25,28,32,33,36,39,40,43,44,45,48,52,55,

%T 56,60,61,63,64,68,69,72,73,75,76,80,81,84,88,91,92,96,99,100,104,105,

%U 108,109,111,112,115,116,120,124,128,132,133,136,140,141,144

%N Sums of two primes whose difference is squarefree.

%e 5 is in the sequence since 5 = 2 + 3 (both prime) and 3 - 2 = 1 is squarefree.

%e 8 is in the sequence since 8 = 5 + 3 (both prime) and 5 - 3 = 2 is squarefree.

%t Flatten[Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]) MoebiusMu[n - 2 i]^2, {i, Floor[(n - 1)/2]}] > 0, n, {}], {n, 150}]]

%Y Cf. A309152.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, Jul 20 2019