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A323024
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Numbers with exactly three distinct exponents in their prime factorization, or three distinct parts in their prime signature.
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9
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360, 504, 540, 600, 720, 756, 792, 936, 1008, 1176, 1188, 1200, 1224, 1350, 1368, 1400, 1404, 1440, 1500, 1584, 1620, 1656, 1836, 1872, 1960, 2016, 2052, 2088, 2160, 2200, 2232, 2250, 2268, 2352, 2400, 2448, 2484, 2520, 2600, 2646, 2664, 2736, 2800, 2880, 2904
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OFFSET
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1,1
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COMMENTS
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The asymptotic density of this sequence is (6/Pi^2) * Sum_{n>=2, n squarefree} r(n)/((n-1)*psi(n)) = 0.030575..., where psi is the Dedekind psi function (A001615), and r(n) = Sum_{d|n, 1<d<n} 1/(d-1) (Sanna, 2020). - Amiram Eldar, Oct 18 2020
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LINKS
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EXAMPLE
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1500 = 2^2 * 3^1 * 5^3 has three distinct exponents {1, 2, 3}, so belongs to the sequence.
52500 = 2^2 * 3^1 * 5^4 * 7^1 has three distinct exponents {1, 2, 4}, so belongs to the sequence.
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MATHEMATICA
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tom[n_]:=Length[Union[Last/@If[n==1, {}, FactorInteger[n]]]];
Select[Range[1000], tom[#]==3&]
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PROG
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CROSSREFS
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Cf. A001221, A001222, A001615, A006939, A033992, A059404, A062770, A071625, A118914, A181819, A323014, A323022, A323025.
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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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