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A309277
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Sums of two primes whose difference is squarefree.
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1
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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