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%I #22 Jan 10 2022 11:09:26
%S 1,2,6,24,120,720,5040,45360,498960,6486480,110270160,2095133040,
%T 41902660800,963761198400,26985313555200,782574093100800,
%U 24259796886124800,897612484786617600,36802111876251321600,1582490810678806828800,74377068101903920953600,3941984609400907810540800
%N 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.
%C Known ratios are 2,3,4,5,6,7,9,11,13,17,19,20,23,28,29,31,37,41,43,47,53.
%e a(2) is 2 because 1*2=2 is highly composite.
%e a(3) is 6 because 2*3=6 is highly composite.
%e a(8) cannot be 5040*8=40320 because 40320 is not a highly composite number.
%t 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 *)
%Y Cf. A002182.
%K nonn
%O 1,2
%A _J. Lowell_, Dec 14 2021
%E More terms from _Amiram Eldar_, Dec 14 2021
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