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A306491
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Numbers that set a record for the number of distinct prime signatures represented among their divisors (A085082).
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1
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1, 2, 4, 8, 12, 24, 48, 96, 144, 192, 288, 480, 576, 720, 1152, 1440, 2880, 4320, 5760, 8640, 11520, 17280, 34560, 51840, 69120, 103680, 120960, 138240, 207360, 241920, 345600, 362880, 414720, 483840, 604800, 725760, 829440, 967680, 1209600, 1451520, 1814400
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listen;
history;
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OFFSET
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1,2
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COMMENTS
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The records are 1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 15, 16, 18, 19, 21, 24, 29, 30, 34, 37, 39, 44, 51, 52, 58, 61, 62, 65, 70, ... (see the link for more values).
Numbers that set a record for the number of divisors of least prime signature (A322584). - Hal M. Switkay, Aug 20 2024
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LINKS
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MATHEMATICA
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ps[1] = {}; ps[n_] := FactorInteger[n][[All, 2]] // Sort; a[n_] := ps /@ Divisors[n] // Union // Length; s={}; am=0; Do[a1=a[n]; If[a1>am, am=a1; AppendTo[s, n]], {n, 1, 2*10^6}]; s (* after Jean-François Alcover at A085082 *)
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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