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A120108 Number triangle T(n,k) = lcm(1,..,n+1)/lcm(1,..,k+1).

%I A120108 #17 May 05 2023 01:43:59
%S A120108 1,2,1,6,3,1,12,6,2,1,60,30,10,5,1,60,30,10,5,1,1,420,210,70,35,7,7,1,
%T A120108 840,420,140,70,14,14,2,1,2520,1260,420,210,42,42,6,3,1,2520,1260,420,
%U A120108 210,42,42,6,3,1,1,27720,13860,4620,2310,462,462,66,33,11,11,1
%N A120108 Number triangle T(n,k) = lcm(1,..,n+1)/lcm(1,..,k+1).
%H A120108 Muniru A Asiru, <a href="/A120108/b120108.txt">Rows n=0..100 of triangle, flattened</a>
%F A120108 Number triangle T(n,k) = [k<=n]*lcm(1,..,n+1)/lcm(1,..,k+1).
%e A120108 Triangle begins:
%e A120108     1;
%e A120108     2,   1;
%e A120108     6,   3,  1;
%e A120108    12,   6,  2,  1;
%e A120108    60,  30, 10,  5, 1;
%e A120108    60,  30, 10,  5, 1, 1;
%e A120108   420, 210, 70, 35, 7, 7, 1;
%p A120108 T:= (n,k)-> ilcm(seq(q,q=1..n+1))/ilcm(seq(r,r=1..k+1)):
%p A120108 seq(seq(T(n,k),k=0..n),n=0..10); # _Muniru A Asiru_, Feb 26 2019
%t A120108 f[n_] := f[n] = LCM @@ Range[n];
%t A120108 T[n_, k_] := f[n+1]/f[k+1];
%t A120108 Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Mar 01 2021 *)
%o A120108 (GAP) Flat(List([0..10],n->List([0..n],k->Lcm(List([1..n+1],i->i))/Lcm(List([1..k+1],i->i))))); # _Muniru A Asiru_, Feb 26 2019
%o A120108 (Magma)
%o A120108 A120108:= func< n,k | Lcm([1..n+1])/Lcm([1..k+1]) >;
%o A120108 [A120108(n,k): k in [0..n], n in [0..12]]; // _G. C. Greubel_, May 04 2023
%o A120108 (SageMath)
%o A120108 def f(n): return lcm(range(1,n+2))
%o A120108 def A120108(n,k):
%o A120108     return f(n)/f(k)
%o A120108 flatten([[A120108(n,k) for k in range(n+1)] for n in range(13)]) # _G. C. Greubel_, May 04 2023
%Y A120108 First column is A003418(n+1). Second column is A025555. Row sums are A120109. Diagonal sums are A120110. Inverse is A120111.
%K A120108 easy,nonn,tabl
%O A120108 0,2
%A A120108 _Paul Barry_, Jun 09 2006