cp's OEIS Frontend

A216917 Square array read by antidiagonals, T(N,n) = lcm{1<=j<=N, gcd(j,n)=1 | j} for N >= 0, n >= 1.

%I A216917 #20 Mar 04 2018 17:47:27
%S A216917 1,1,1,2,1,1,6,1,1,1,12,3,2,1,1,60,3,2,1,1,1,60,15,4,3,2,1,1,420,15,
%T A216917 20,3,6,1,1,1,840,105,20,15,12,1,2,1,1,2520,105,140,15,12,1,6,1,1,1,
%U A216917 2520,315,280,105,12,5,12,3,2,1,1,27720,315,280,105,84
%N A216917 Square array read by antidiagonals, T(N,n) = lcm{1<=j<=N, gcd(j,n)=1 | j} for N >= 0, n >= 1.
%C A216917 T(N,n) is the least common multiple of all integers up to N that are relatively prime to n.
%C A216917 Replacing LCM in the definition with "product" gives the Gauss factorial A216919.
%F A216917 For n > 0:
%F A216917 A(n,1) = A003418(n);
%F A216917 A(n,2^k) = A217858(n) for k > 0;
%F A216917 A(n,3^k) = A128501(n-1) for k > 0;
%F A216917 A(2,n) = A000034(n);
%F A216917 A(3,n) = A129203(n-1);
%F A216917 A(4,n) = A129197(n-1);
%F A216917 A(n,n) = A038610(n);
%F A216917 A(floor(n/2),n) = A124443(n);
%F A216917 A(n,1)/A(n,n) = A064446(n);
%F A216917 A(n,1)/A(n,2) = A053644(n).
%e A216917    n | N=0 1 2 3  4  5  6   7   8    9   10
%e A216917 -----+-------------------------------------
%e A216917    1 |   1 1 2 6 12 60 60 420 840 2520 2520
%e A216917    2 |   1 1 1 3  3 15 15 105 105  315  315
%e A216917    3 |   1 1 2 2  4 20 20 140 280  280  280
%e A216917    4 |   1 1 1 3  3 15 15 105 105  315  315
%e A216917    5 |   1 1 2 6 12 12 12  84 168  504  504
%e A216917    6 |   1 1 1 1  1  5  5  35  35   35   35
%e A216917    7 |   1 1 2 6 12 60 60  60 120  360  360
%e A216917    8 |   1 1 1 3  3 15 15 105 105  315  315
%e A216917    9 |   1 1 2 2  4 20 20 140 280  280  280
%e A216917   10 |   1 1 1 3  3  3  3  21  21   63   63
%e A216917   11 |   1 1 2 6 12 60 60 420 840 2520 2520
%e A216917   12 |   1 1 1 1  1  5  5  35  35   35   35
%e A216917   13 |   1 1 2 6 12 60 60 420 840 2520 2520
%t A216917 t[_, 0] = 1; t[n_, k_] := LCM @@ Select[Range[k], CoprimeQ[#, n]&]; Table[t[n - k + 1, k], {n, 0, 11}, {k, n, 0, -1}] // Flatten (* _Jean-François Alcover_, Jul 29 2013 *)
%o A216917 (Sage)
%o A216917 def A216917(N, n):
%o A216917     return lcm([j for j in (1..N) if gcd(j, n) == 1])
%o A216917 for n in (1..13): [A216917(N,n) for N in (0..10)]
%K A216917 nonn,tabl
%O A216917 1,4
%A A216917 _Peter Luschny_, Oct 02 2012