Voozh

A120942

3-smooth numbers 2^i*3^j where i and j are regular 3-smooth numbers.

6, 12, 18, 24, 36, 48, 54, 72, 108, 144, 162, 192, 216, 324, 432, 576, 648, 768, 1296, 1458, 1536, 1728, 2304, 2916, 4608, 5184, 5832, 6912, 11664, 12288, 13122, 13824, 20736, 26244, 36864, 39366, 41472, 46656, 52488, 78732, 104976, 110592, 157464, 186624, 196608, 314928, 331776, 373248, 419904, 589824, 786432

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

54 is in the list because it is 2^1*3^3 and 1 and 3 are 3-smooth numbers.

MAPLE

interface(prettyprint=0) ; isA003586 := proc(n) local ifa, f, bas ; ifa := op(2, ifactors(n)) ; for f from 1 to nops(ifa) do bas := op(1, op(f, ifa)) ; if bas > 3 then RETURN(false) ; fi ; od ; RETURN(true) ; end: isA120942 := proc(n) local ifa, f, bas, expo ; ifa := op(2, ifactors(n)) ; if nops(ifa) <> 2 then RETURN(false) ; fi ; for f from 1 to nops(ifa) do bas := op(1, op(f, ifa)) ; if bas > 3 then RETURN(false) ; else expo := op(2, op(f, ifa)) ; if not isA003586(expo) then RETURN(false) ; fi ; fi ; od ; RETURN(true) ; end: for n from 2 to 40000 do if isA120942(n) then printf("%d, ", n) ; fi ; od; # R. J. Mathar, Aug 23 2006

MATHEMATICA

maxTerm = 10^6;

maxExponent = Log2[maxTerm] // Floor;

ee = Select[Range[maxExponent], FactorInteger[#][[-1, 1]] <= 3&];

ff = Flatten[Table[{{2, i}, {3, j}}, {i, ee}, {j, ee}], 1];

okQ[n_] := MemberQ[ff, FactorInteger[n]];

Select[Range[maxTerm], okQ] (* Jean-François Alcover, Aug 24 2024 *)

CROSSREFS

Cf. A003586.

Sequence in context: A033845 A187778 A344471 * A147306 A359957 A031478

Adjacent sequences: A120939 A120940 A120941 * A120943 A120944 A120945

KEYWORD