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A366854
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Powers k^m such that k is neither squarefree nor prime powers, and m > 1.
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1
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144, 324, 400, 576, 784, 1296, 1600, 1728, 1936, 2025, 2304, 2500, 2704, 2916, 3136, 3600, 3969, 4624, 5184, 5625, 5776, 5832, 6400, 7056, 7744, 8000, 8100, 8464, 9216, 9604, 9801, 10000, 10816, 11664, 12544, 13456, 13689, 13824, 14400, 15376, 15876, 17424, 18225
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OFFSET
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1,1
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COMMENTS
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Analogous to A303606 = { k^m : Omega(k) = omega(k) > 1, m > 1 }, i.e., squarefree composite k (in A120944) raised to m > 1. Proper subset of A131605, itself a proper subset of A286708, which is in turn a proper subset of A126706. This sequence does not intersect Achilles numbers A052486.
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LINKS
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FORMULA
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This sequence is A126706(i)^m, m > 1.
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EXAMPLE
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a(1) = b(1)^2 = 12^2 = 144. Since 144 = 2^4*3^2, it is both powerful and a perfect power.
a(2) = b(2)^2 = 18^2 = 324.
a(3) = b(3)^2 = 20^2 = 400.
a(8) = b(1)^3 = 12^3 = 1728, etc.
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MATHEMATICA
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nn = 20000; i = 1; k = 2;
MapIndexed[Set[S[First[#2]], #1] &,
Select[Range@ Sqrt[nn], Nor[SquareFreeQ[#], PrimePowerQ[#]] &] ];
Union@ Reap[
While[j = 2;
While[S[i]^j < nn, Sow[S[i]^j]; j++]; j > 2,
k++; i++] ][[-1, 1]]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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