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EXAMPLE
| For n=2, 3, 4, 5, 7: {2^2, 6, 3^2}, {5^2, 30, 7^2}, {13^2, 210, 17^2}, {47^2, 2310, 53^2} {709^2, 510510, 719^2} or {4, 6, 9}, {25, 30, 49}, {169, 210, 289}, {2209, 2310, 2809}, {502681, 510510, 516961}. Also, if n=2, then a[2]<p(1)=2, if n=3, then a[3]=p(3)=5 but for n>3, a[n]>p(n+1), e.g. a[6]=p(40)=p(6+34)=173.
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MATHEMATICA
| q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]] rq[x_] := Floor[Sqrt[q[w]]//N] Table[Prime[PrimePi[a[w]]], {w, 2, 15}]
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