A309277 Sums of two primes whose difference is squarefree.

5, 7, 8, 9, 12, 15, 16, 19, 20, 21, 24, 25, 28, 32, 33, 36, 39, 40, 43, 44, 45, 48, 52, 55, 56, 60, 61, 63, 64, 68, 69, 72, 73, 75, 76, 80, 81, 84, 88, 91, 92, 96, 99, 100, 104, 105, 108, 109, 111, 112, 115, 116, 120, 124, 128, 132, 133, 136, 140, 141, 144

Offset: 1

Author

Wesley Ivan Hurt, Jul 20 2019

Keywords

• nonn

Examples

			5 is in the sequence since 5 = 2 + 3 (both prime) and 3 - 2 = 1 is squarefree.
8 is in the sequence since 8 = 5 + 3 (both prime) and 5 - 3 = 2 is squarefree.
		

Crossrefs

Cf. A309152.

Programs

Mathematica

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}]]