A181804 List 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

Offset

1,2

Comments

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Achim Flammenkamp, List of the first 1200 highly composite numbers.

Eric Weisstein's World of Mathematics, Highly composite number.

Eric Weisstein's World of Mathematics, Least Common Multiple (LCM).

Eric Weisstein's World of Mathematics, Proper Divisor.

Example

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.

Mathematica

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 *)

Crossrefs

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

Subsequence of A025487.

Includes all members of A181806.

Cf. A002182, A181802.

Sequence in context: A056795 A141420 A141551 * A094348 A242298 A002182

Adjacent sequences: A181801 A181802 A181803 * A181805 A181806 A181807

Keyword

nonn

Author

Matthew Vandermast, Nov 27 2010

Status

approved