A309292 Numbers that can be written as the sum of two primes, p, q, where p < q such that q^2 - p^2 is squarefree.
5, 7, 15, 19, 21, 33, 39, 43, 55, 61, 69, 73, 91, 105, 109, 111, 115, 133, 141, 159, 165, 181, 183, 195, 199, 201, 213, 231, 235, 241, 253, 259, 271, 273, 285, 295, 309, 313, 339, 349, 381, 385, 399, 403, 411, 421, 433, 435, 451, 465, 469, 489, 493, 501, 505
Offset: 1
Keywords
Examples
5 is in the sequence since 5 = 2 + 3 (both prime) and since 3^2 - 2^2 = 5 is squarefree. 7 is in the sequence since 7 = 2 + 5 (both prime) and since 5^2 - 2^2 = 21 is squarefree.
Crossrefs
Cf. A309277.
Programs
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Mathematica
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}]]