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A303661
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Powers of squarefree semiprimes that are not squarefree.
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3
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36, 100, 196, 216, 225, 441, 484, 676, 1000, 1089, 1156, 1225, 1296, 1444, 1521, 2116, 2601, 2744, 3025, 3249, 3364, 3375, 3844, 4225, 4761, 5476, 5929, 6724, 7225, 7396, 7569, 7776, 8281, 8649, 8836, 9025, 9261, 10000, 10648, 11236, 12321, 13225, 13924, 14161, 14884
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Squarefree.
Eric Weisstein's World of Mathematics, Semiprime.
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FORMULA
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Sum_{n>=1} 1/a(n) = Sum_{n>=1} 1/((A006881(n)-1)*A006881(n)) = Sum_{k>=2} (P(k)^2 - P(2*k))/2 = 0.07160601536406295068..., where P(k) is the prime zeta function. - Amiram Eldar, Feb 12 2021
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EXAMPLE
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1089 is in the sequence because 1089 = 3^2*11^2.
1296 is in the sequence because 1296 = 2^4*3^4.
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MATHEMATICA
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Select[Range[15000], Length[Union[FactorInteger[#][[All, 2]]]] == 1 && PrimeNu[#] == 2 && ! SquareFreeQ[#] &]
seq[max_] := Module[{sp = Select[Range[Floor@Sqrt[max]], SquareFreeQ[#] && PrimeNu[#] == 2 &], s = {}}, Do[s = Join[s, sp[[k]]^Range[2, Floor@Log[sp[[k]], max]]], {k, 1, Length[sp]}]; Union@s]; seq[10000] (* Amiram Eldar, Feb 12 2021 *)
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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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