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A350113
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a(1)=1; for n>1 a(n) is the smallest highly composite number (A002182) that is a multiple of a(n-1) where the ratios are strictly increasing.
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0
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1, 2, 6, 24, 120, 720, 5040, 45360, 498960, 6486480, 110270160, 2095133040, 41902660800, 963761198400, 26985313555200, 782574093100800, 24259796886124800, 897612484786617600, 36802111876251321600, 1582490810678806828800, 74377068101903920953600, 3941984609400907810540800
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OFFSET
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1,2
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COMMENTS
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Known ratios are 2,3,4,5,6,7,9,11,13,17,19,20,23,28,29,31,37,41,43,47,53.
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LINKS
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EXAMPLE
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a(2) is 2 because 1*2=2 is highly composite.
a(3) is 6 because 2*3=6 is highly composite.
a(8) cannot be 5040*8=40320 because 40320 is not a highly composite number.
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MATHEMATICA
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hcn = Import["https://oeis.org/A002182/b002182.txt", "Table"][[;; , 2]]; seq = {1}; m = ratio = ratioPrev = 1; Do[k = FirstCase[hcn, _?(Divisible[#, m] && (ratio = #/m) > ratioPrev &)]; AppendTo[seq, k]; m = k; ratioPrev = ratio, {21}]; seq (* Amiram Eldar, Dec 16 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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EXTENSIONS
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STATUS
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approved
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