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A290399
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Number of solutions to Diophantine equation x + y + z = prime(n) with x*y*z = k^3 (0 < x <= y <= z).
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0
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0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 2, 3, 2, 1, 3, 2, 2, 2, 3, 1, 2, 3, 3, 3, 4, 3, 5, 2, 1, 5, 1, 4, 3, 3, 3, 3, 4, 5, 3, 3, 6, 3, 2, 3, 5, 5, 3, 6, 8, 2, 3, 7, 5, 7, 3, 5, 7, 5, 4, 1, 7, 4, 1, 8, 6, 5, 4, 5, 4, 7, 4, 9, 6, 6, 5, 8, 5, 7, 6, 4
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OFFSET
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1,11
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LINKS
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EXAMPLE
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a(11) = 2 because the equation x + y + z = 31 (prime(11)) has exactly 2 solutions with x*y*z = k^3: (x, y, z) = (1, 5, 25) and (1, 12, 18), which satisfy 1*5*25 = 5^3 and 1*12*18 = 6^3.
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MATHEMATICA
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a[n_] := Length@ Select[ IntegerPartitions[ Prime[n], {3}], IntegerQ[ (Times @@ #)^(1/3)] &]; Array[a, 50] (* Giovanni Resta, Aug 07 2017 *)
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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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