A096075 Least common multiple of first n 3-smooth numbers.

1, 2, 6, 12, 12, 24, 72, 72, 144, 144, 144, 432, 864, 864, 864, 864, 1728, 1728, 5184, 5184, 5184, 10368, 10368, 10368, 10368, 10368, 31104, 62208, 62208, 62208, 62208, 62208, 62208, 124416, 124416, 124416, 373248, 373248, 373248, 373248, 746496

Offset: 1

Author

Reinhard Zumkeller, Jul 21 2004

Keywords

• nonn

Comments

Subsequence of A003586.

Examples

			The first seven 3-smooth numbers are {1, 2, 3, 4, 6, 8, 9} and their lcm is 72. - _David A. Corneth_, Jul 13 2023
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to lcm's.

Crossrefs

Cf. A003418, A003586, A006899, A022330, A022331, A051451.

Programs

Mathematica

seq[max_] := Module[{sm3 = Sort[Flatten[Table[2^i*3^j, {i, 0, Log2[max]}, {j, 0, Log[3, max/2^i]}]]], e2, e3}, e2 = FoldList[Max, IntegerExponent[sm3, 2]]; e3 = FoldList[Max, IntegerExponent[sm3, 3]]; 2^e2*3^e3]; seq[1000] (* Amiram Eldar, Jul 13 2023 *)

Formula

a(n) > a(n-1) iff A003586(n) is a power of 2 or of 3 (cf. A006899, A022330, A022331).