A062723 - OEIS

%I #29 Oct 04 2024 11:57:20

%S 1,1,2,6,12,12,36,36,36,108,108,108,324,324,324,972,972,972,2916,2916,

%T 2916,8748,8748,8748,26244,26244,26244,78732,78732,78732,236196,

%U 236196,236196,708588,708588,708588,2125764,2125764,2125764,6377292,6377292

%N Least common multiple (LCM) of the first n+1 terms of A000792.

%C Apparently this sequence (when taken without repeats) is a subsequence of A000792, cf. A202337.

%H Harry J. Smith, <a href="/A062723/b062723.txt">Table of n, a(n) for n = 0..400</a>

%H <a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 3).

%F a(n) = 4*3^floor(n/3), n >= 3. - _Vladeta Jovovic_, Jul 18 2001

%F G.f.: (1+x+2*x^2+3*x^3+9*x^4+6*x^5+18*x^6)/(1-3*x^3).

%e a(4)=12 because a(4) is the LCM of 1,1,2,3,4 - which is clearly 12.

%t Module[{nn=50,trms},trms=CoefficientList[Series[(1+x+2x^2+x^4)/(1-3x^3),{x,0,nn}],x];Table[LCM@@Take[trms,n],{n,nn}]] (* or *) LinearRecurrence[{0,0,3},{1,1,2,6,12,12,36},50] (* _Harvey P. Dale_, Oct 04 2024 *)

%o (PARI) a(n)=if(n<0,0,if(n<4,n!,4*3^(n\3)))

%o (Haskell)

%o a062723 n = a062723_list !! n

%o a062723_list = scanl1 lcm a000792_list

%o -- _Reinhard Zumkeller_, Dec 17 2011

%Y Cf. A000244, A000792.

%K easy,nonn

%O 0,3

%A Felix Goldberg (felixg(AT)tx.technion.ac.il), Jul 15 2001

%E Formula and correction from _Vladeta Jovovic_, Jul 18 2001

%E More terms from _Jason Earls_, Jul 21 2001