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A216915 T(n, k) = Product{1<=j<=n, gcd(j,k)=1 | j} / lcm{1<=j<=n, gcd(j,k)=1 | j} for n >= 0, k >= 1, square array read by antidiagonals. 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 12, 1, 2, 1, 1, 1, 1, 12, 1, 2, 1, 1, 1, 1, 1, 48, 1, 2, 1, 2, 1, 1, 1, 1, 144, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1440, 3, 8, 1, 12, 1, 2, 1, 1, 1, 1, 1440, 3, 8, 1, 12, 1, 2, 1, 1, 1, 1, 1, 17280, 3, 80 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

T(n,k) = Product(R(n,k))/lcm(R(n,k)) where R(n,k) is the set of all integers up to n that are relatively prime to k.

T(n,k) = A216919(n,k)/A216917(n,k).

LINKS

Table of n, a(n) for n=1..81.

FORMULA

For n > 0:

A(n,1) = A025527(n);

A(4,n) = A000034(n);

A(n,n) = A128247(n).

EXAMPLE

   k |n=0  1  2  3  4  5  6  7  8   9   10

  ---+------------------------------------

   1 |  1  1  1  1  2  2 12 12 48 144 1440

   2 |  1  1  1  1  1  1  1  1  1   3    3

   3 |  1  1  1  1  2  2  2  2  8   8   80

   4 |  1  1  1  1  1  1  1  1  1   3    3

   5 |  1  1  1  1  2  2 12 12 48 144  144

   6 |  1  1  1  1  1  1  1  1  1   1    1

   7 |  1  1  1  1  2  2 12 12 48 144 1440

   8 |  1  1  1  1  1  1  1  1  1   3    3

   9 |  1  1  1  1  2  2  2  2  8   8   80

  10 |  1  1  1  1  1  1  1  1  1   3    3

  11 |  1  1  1  1  2  2 12 12 48 144 1440

  12 |  1  1  1  1  1  1  1  1  1   1    1

  13 |  1  1  1  1  2  2 12 12 48 144 1440

PROG

(Sage)

def A216915(n, k):

    def R(n, k): return [j for j in (1..n) if gcd(j, k) == 1]

    return mul(R(n, k))/lcm(R(n, k))

for k in (1..13): [A216915(n, k) for n in (0..10)]

CROSSREFS

Sequence in context: A304886 A295632 A139549 * A280569 A140345 A177706

Adjacent sequences:  A216912 A216913 A216914 * A216916 A216917 A216918

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Oct 02 2012

STATUS

approved

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Last modified July 12 11:25 EDT 2020. Contains 335658 sequences. (Running on oeis4.)