Amiram Eldar, <a href="/A181804/b181804_1.txt">Table of n, a(n) for n = 1..10000</a>

reviewed

approved

proposed

reviewed

editing

proposed

Amiram Eldar, <a href="/A181804/b181804_1.txt">Table of n, a(n) for n = 1..10000</a>

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 *)

Cf. A002182, A181802.

A. Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.txt">List of the first 1200 highly composite numbers</a>.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly composite number</a>.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LeastCommonMultiple.html">Least Common Multiple</a> (LCM).

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ProperDivisor.html">Proper Divisor</a>.

Subsequence of A025487. Includes all members of A181806.

Includes all members of A181806.

Cf. A002182.

approved

editing

_Matthew Vandermast (ghodges14(AT)comcast.net), _, Nov 27 2010

proposed

approved

allocated for Matthew VandermastList of numbers that are LCMs of some set of highly composite numbers (A002182).

1, 2, 4, 6, 12, 24, 36, 48, 60, 72, 120, 144, 180, 240, 360, 720, 840, 1260, 1680, 2520, 5040, 7560, 10080, 15120, 20160, 25200, 27720, 30240, 45360, 50400, 55440, 60480, 75600, 83160, 90720, 100800, 110880, 151200, 166320, 181440, 221760, 226800, 277200

1,2

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.

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.

A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.txt">List of the first 1200 highly composite numbers</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HighlyCompositeNumber.html">Highly composite number</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LeastCommonMultiple.html">Least Common Multiple</a> (LCM)

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ProperDivisor.html">Proper Divisor</a>

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.

A181805 gives the number of highly composite divisors of a(n), or A181801(a(n)).

Subsequence of A025487. Includes all members of A181806.

allocated

nonn

Matthew Vandermast (ghodges14(AT)comcast.net), Nov 27 2010

approved

proposed