A124443 -id:A124443 - 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.

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, 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, 2520, 315, 280, 105, 12, 5, 12, 3, 2, 1, 1, 27720, 315, 280, 105, 84

Offset: 1

Peter Luschny, Oct 02 2012

T(N,n) is the least common multiple of all integers up to N that are relatively prime to n.

Replacing LCM in the definition with "product" gives the Gauss factorial A216919.

			   n | N=0 1 2 3  4  5  6   7   8    9   10
-----+-------------------------------------
   1 |   1 1 2 6 12 60 60 420 840 2520 2520
   2 |   1 1 1 3  3 15 15 105 105  315  315
   3 |   1 1 2 2  4 20 20 140 280  280  280
   4 |   1 1 1 3  3 15 15 105 105  315  315
   5 |   1 1 2 6 12 12 12  84 168  504  504
   6 |   1 1 1 1  1  5  5  35  35   35   35
   7 |   1 1 2 6 12 60 60  60 120  360  360
   8 |   1 1 1 3  3 15 15 105 105  315  315
   9 |   1 1 2 2  4 20 20 140 280  280  280
  10 |   1 1 1 3  3  3  3  21  21   63   63
  11 |   1 1 2 6 12 60 60 420 840 2520 2520
  12 |   1 1 1 1  1  5  5  35  35   35   35
  13 |   1 1 2 6 12 60 60 420 840 2520 2520

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 *)

def A216917(N, n):
    return lcm([j for j in (1..N) if gcd(j, n) == 1])
for n in (1..13): [A216917(N,n) for N in (0..10)]

For n > 0:
A(n,1) = A003418(n);
A(n,2^k) = A217858(n) for k > 0;
A(n,3^k) = A128501(n-1) for k > 0;
A(2,n) = A000034(n);
A(3,n) = A129203(n-1);
A(4,n) = A129197(n-1);
A(n,n) = A038610(n);
A(floor(n/2),n) = A124443(n);
A(n,1)/A(n,n) = A064446(n);
A(n,1)/A(n,2) = A053644(n).

A124444 a(n) = LCM of the integers, from n/2 to n, which are coprime to n.

Original entry on oeis.org

1, 1, 2, 3, 12, 5, 60, 35, 280, 63, 2520, 77, 27720, 1287, 8008, 6435, 720720, 2431, 12252240, 46189, 3695120, 440895, 232792560, 96577, 1070845776, 3900225, 2974571600, 5014575, 80313433200, 215441, 2329089562800, 31556720475

Offset: 1

Leroy Quet, Nov 01 2006

nonn

			The integers which are >= 9/2 and are <= 9 and which are coprime to 9 are 5, 7 and 8. So a(9) = lcm(5,7,8) = 280.

Cf. A124443.

f[n_] := LCM @@ Select[Range[Ceiling[n/2], n], GCD[ #, n] == 1 &];Table[f[n], {n, 33}] (* Ray Chandler, Nov 12 2006 *)

a(n) = lcm(select(x->(gcd(x, n)==1), vector(n\2, k, n\2+k))); \\ Michel Marcus, Mar 18 2018

Extended by Ray Chandler, Nov 12 2006

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.

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