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A140999
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Members of A067128 that are the smallest numbers with their prime signatures.
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5
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1, 2, 4, 6, 8, 12, 24, 30, 36, 48, 60, 72, 96, 120, 180, 240, 360, 420, 480, 720, 840, 1080, 1260, 1440, 1680, 2160, 2520, 3360, 4320, 4620, 5040, 7560, 9240, 10080, 12600, 13860, 15120, 18480, 20160, 25200, 27720, 30240, 36960, 37800, 40320, 45360
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OFFSET
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1,2
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COMMENTS
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Conjecture (false!): includes all members of A094348.
Counterexample to conjecture: 5354228880, the smallest positive multiple of the first 23 positive integers, does not belong to A067128. It is the smallest member of A003418 (a subsequence of A094348) not to be largely composite.
Includes all members of A097212. (End)
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LINKS
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EXAMPLE
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3 doesn't qualify because it's not the smallest number with its prime signature. 16 does not qualify because it's not a member of A067128.
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MATHEMATICA
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PrimeExponents[n_] := Last /@ FactorInteger[n]; lpe = {}; ln = {1}; dm=1; Do[d=DivisorSigma[0, n]; If[d>=dm, dm=d; pe = Sort@PrimeExponents@n; If[ FreeQ[lpe, pe], AppendTo[lpe, pe]; AppendTo[ln, n]]], {n, 2, 50000}]; ln (* Amiram Eldar, Jun 20 2019 after Robert G. Wilson v at A025487 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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