cp's OEIS Frontend

A181804 List of numbers that are LCMs of some set of highly composite numbers (A002182).

%I A181804 #12 Feb 16 2025 08:33:13
%S A181804 1,2,4,6,12,24,36,48,60,72,120,144,180,240,360,720,840,1260,1680,2520,
%T A181804 5040,7560,10080,15120,20160,25200,27720,30240,45360,50400,55440,
%U A181804 60480,75600,83160,90720,100800,110880,151200,166320,181440,221760,226800,277200
%N A181804 List of numbers that are LCMs of some set of highly composite numbers (A002182).
%C A181804 Numbers n such that A181801(n) is higher than A181801(d) for any proper divisor d of n. Also, numbers n such that row n of A181802 is identical to no previous row of A181802.
%C A181804 A002182 is a proper subsequence of this sequence. 72 is the first LCM of some set of highly composite numbers that is not itself highly composite.
%H A181804 Amiram Eldar, <a href="/A181804/b181804.txt">Table of n, a(n) for n = 1..10000</a>
%H A181804 Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.txt">List of the first 1200 highly composite numbers</a>.
%H A181804 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly composite number</a>.
%H A181804 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LeastCommonMultiple.html">Least Common Multiple</a> (LCM).
%H A181804 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ProperDivisor.html">Proper Divisor</a>.
%e A181804 1, 2, 4, 6, 12, 24 and 36 are all highly composite numbers, and their least common multiple (LCM) is 72.  Hence, 72 is a member of the sequence.
%t A181804 seq[max_] := Module[{hcn = {}, hcnmax, d, dm = 0, s = {1}}, Do[d = DivisorSigma[0, n]; If[d > dm, dm = d; AppendTo[hcn, n]], {n, 1, max}]; hcnmax = hcn[[-1]]; Do[s = Union[Join[s, Select[LCM[hcn[[k]], s], # <= hcnmax &]]], {k, 2, Length[hcn]}]; s]; seq[300000] (* _Amiram Eldar_, Jun 23 2023 *)
%Y A181804 A181805 gives the number of highly composite divisors of a(n), or A181801(a(n)).
%Y A181804 Subsequence of A025487.
%Y A181804 Includes all members of A181806.
%Y A181804 Cf. A002182, A181802.
%K A181804 nonn
%O A181804 1,2
%A A181804 _Matthew Vandermast_, Nov 27 2010