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A216917 Square array read by antidiagonals, T(N,n) = lcm{1<=j<=N, gcd(j,n)=1 | j} for N >= 0, n >= 1. 4
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..71.

FORMULA

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).

EXAMPLE

   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

MATHEMATICA

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-Fran├žois Alcover, Jul 29 2013 *)

PROG

(Sage)

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)]

CROSSREFS

Sequence in context: A245567 A204168 A216914 * A216919 A152656 A096162

Adjacent sequences:  A216914 A216915 A216916 * A216918 A216919 A216920

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Oct 02 2012

STATUS

approved

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Last modified June 6 14:04 EDT 2020. Contains 334827 sequences. (Running on oeis4.)