A167192 Triangle read by rows: T(n,k) = (n-k)/gcd(n,k), 1 <= k <= n.

0, 1, 0, 2, 1, 0, 3, 1, 1, 0, 4, 3, 2, 1, 0, 5, 2, 1, 1, 1, 0, 6, 5, 4, 3, 2, 1, 0, 7, 3, 5, 1, 3, 1, 1, 0, 8, 7, 2, 5, 4, 1, 2, 1, 0, 9, 4, 7, 3, 1, 2, 3, 1, 1, 0, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 5, 3, 2, 7, 1, 5, 1, 1, 1, 1, 0, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 6, 11, 5, 9, 4, 1, 3, 5, 2, 3

Offset

1,4

Comments

T(n,k) = A025581(n,k)/A050873(n,k);

T(n,1) = A001477(n-1);

T(n,2) = A026741(n-2) for n > 1;

T(n,3) = A051176(n-3) for n > 2;

T(n,4) = A060819(n-4) for n > 4;

T(n,n-3) = A144437(n) for n > 3;

T(n,n-2) = A000034(n) for n > 2;

T(n,n-1) = A000012(n);

T(n,n) = A000004(n).

Links

Indranil Ghosh, Rows 1..120 of triangle, flattened

Formula

T(n,k) = (n-k)/gcd(n,k), 1 <= k <= n.

Example

The triangle T(n,k) begins:
n\k   1   2   3   4  5  6  7  8  9 10 11 12 13  14  15 ...
1:    0
2:    1   0
3:    2   1   0
4:    3   1   1   0
5:    4   3   2   1  0
6:    5   2   1   1  1  0
7:    6   5   4   3  2  1  0
8:    7   3   5   1  3  1  1  0
9:    8   7   2   5  4  1  2  1  0
10:   9   4   7   3  1  2  3  1  1  0
11:  10   9   8   7  6  5  4  3  2  1  0
12:  11   5   3   2  7  1  5  1  1  1  1  0
13:  12  11  10   9  8  7  6  5  4  3  2  1  0
14:  13   6  11   5  9  4  1  3  5  2  3  1  1   0
15:  14  13   4  11  2  3  8  7  2  1  4  1  2   1   0
- Wolfdieter Lang, Feb 20 2013

Mathematica

Flatten[Table[(n-k)/GCD[n, k], {n, 20}, {k, n}]] (* Harvey P. Dale, Nov 27 2015 *)

Prog

(PARI) for(n=1, 10, for(k=1, n, print1((n-k)/gcd(n, k), ", "))) \\ G. C. Greubel, Sep 13 2017

Crossrefs

Cf. A164306, A054531.

Sequence in context: A264422 A176808 A327029 * A335435 A363048 A262114

Adjacent sequences: A167189 A167190 A167191 * A167193 A167194 A167195

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Oct 30 2009

Status

approved