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A120109 Row sums of number triangle A120108.

%I A120109 #23 May 05 2023 01:44:09
%S A120109 1,3,10,21,106,107,750,1501,4504,4505,49556,49557,644242,644243,
%T A120109 644244,1288489,21904314,21904315,416181986,416181987,416181988,
%U A120109 416181989,9572185748,9572185749,47860928746,47860928747,143582786242
%N A120109 Row sums of number triangle A120108.
%C A120109 It appears that the indices k such that a(k) = a(k-1) + 1 are A080765. - _Michel Marcus_, Mar 04 2019
%H A120109 Muniru A Asiru, <a href="/A120109/b120109.txt">Table of n, a(n) for n = 0..1000</a>
%F A120109 a(n) = Sum_{k=0..n} lcm(1,...,n+1)/lcm(1,...,k+1).
%t A120109 A120108[n_, k_]:= LCM@@Range[n+1]/(LCM@@Range[k+1]);
%t A120109 A120109[n_]:= Sum[A120108[n, k], {k,0,n}];
%t A120109 Table[A120109[n], {n,0,50}] (* _G. C. Greubel_, May 04 2023 *)
%o A120109 (GAP) List([0..30],n->Sum([0..n],k->Lcm(List([1..n+1],i->i))/Lcm(List([1..k+1],i->i)))); # _Muniru A Asiru_, Mar 03 2019
%o A120109 (PARI) a(n) = lcm([1..n+1])*sum(k=0, n, 1/lcm([1..k+1])); \\ _Michel Marcus_, Mar 04 2019
%o A120109 (Magma)
%o A120109 A120108:= func< n,k | Lcm([1..n+1])/Lcm([1..k+1]) >;
%o A120109 [(&+[A120108(n,k): k in [0..n]]): n in [0..50]]; // _G. C. Greubel_, May 04 2023
%o A120109 (SageMath)
%o A120109 def f(n): return lcm(range(1,n+2))
%o A120109 def A120109(n):
%o A120109     return sum(f(n)//f(k) for k in range(n+1))
%o A120109 [A120109(n) for n in range(51)] # _G. C. Greubel_, May 04 2023
%Y A120109 Cf. A080765, A120108, A120110.
%K A120109 easy,nonn
%O A120109 0,2
%A A120109 _Paul Barry_, Jun 09 2006