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A120112 Row sums of number triangle A120111.

%I A120112 #30 May 10 2023 03:09:26
%S A120112 1,-1,-2,-1,-4,0,-6,-1,-2,0,-10,0,-12,0,0,-1,-16,0,-18,0,0,0,-22,0,-4,
%T A120112 0,-2,0,-28,0,-30,-1,0,0,0,0,-36,0,0,0,-40,0,-42,0,0,0,-46,0,-6,0,0,0,
%U A120112 -52,0,0,0,0,0,-58,0,-60,0,0,-1,0,0,-66,0,0,0,-70,0,-72
%N A120112 Row sums of number triangle A120111.
%C A120112 The last row of the columns in tables A133232 and A133233 are given by this sequence via the formula: if n < k + k*abs(a(n)) then k, otherwise 1 (1 <= k <= n). - _Mats Granvik_, Jan 22 2008
%H A120112 Muniru A Asiru, <a href="/A120112/b120112.txt">Table of n, a(n) for n = 0..5000</a>
%F A120112 a(n) = 1 - lcm(1,...,n+1)/lcm(1,...,n) for n > 0.
%F A120112 a(n) = 1 - A014963(n+1). - _Joerg Arndt_, Sep 12 2016
%t A120112 Table[If[n==0, 1, 1-LCM@@Range[n+1]/(LCM@@Range[n])], {n,0,100}] (* _G. C. Greubel_, May 05 2023 *)
%o A120112 (PARI) a(n) = if (n==0, 1, 1 - lcm(vector(n+1, k, k))/lcm(vector(n, k, k))); \\ _Michel Marcus_, Sep 11 2016
%o A120112 (GAP) Concatenation([1],List([1..70],n->1-Lcm(List([1..n+1],i->i))/Lcm(List([1..n],i->i)))); # _Muniru A Asiru_, Mar 04 2019
%o A120112 (Magma)
%o A120112 A120112:= func< n | n eq 0 select 1 else 1-Lcm([1..n+1])/Lcm([1..n]) >;
%o A120112 [A120112(n): n in [0..100]]; // _G. C. Greubel_, May 05 2023
%o A120112 (SageMath)
%o A120112 def A120112(n):
%o A120112     return 1 if n == 0 else 1 - lcm(range(1,n+2)) // lcm(range(1,n+1))
%o A120112 [A120112(n) for n in range(101)] # _G. C. Greubel_, May 05 2023
%Y A120112 Cf. A014963, A120111, A133232, A133233.
%K A120112 easy,sign
%O A120112 0,3
%A A120112 _Paul Barry_, Jun 09 2006