|
%I #8 Mar 23 2014 03:20:08
%S 6,12,18,24,36,48,54,72,108,144,162,192,216,324,432,576,648,768,1296,
%T 1458,1536,1728,2304,2916,4608,5184,5832,6912,11664,12288,13122,13824,
%U 20736,26244,36864,39366,41472,46656,52488,78732,104976,110592,157464
%N 3-smooth numbers 2^i*3^j where i and j are regular 3-smooth numbers.
%e 54 is in the list because it is 2^1*3^3 and 1 and 3 are 3-smooth numbers.
%p 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
%Y Cf. A003586.
%K nonn
%O 1,1
%A _Ben Paul Thurston_, Aug 18 2006
%E Corrected and extended by _Ray Chandler_ and _R. J. Mathar_, Aug 23 2006
|
