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A096075
Least common multiple of first n 3-smooth numbers.
1
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
1,2
COMMENTS
Subsequence of A003586.
FORMULA
a(n) > a(n-1) iff A003586(n) is a power of 2 or of 3 (cf. A006899, A022330, A022331).
EXAMPLE
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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 21 2004
STATUS
approved