A201146 Triangle read by rows: T(n,k) = (n#)/(k#), 1 <= k <= n.

1, 2, 1, 6, 3, 1, 6, 3, 1, 1, 30, 15, 5, 5, 1, 30, 15, 5, 5, 1, 1, 210, 105, 35, 35, 7, 7, 1, 210, 105, 35, 35, 7, 7, 1, 1, 210, 105, 35, 35, 7, 7, 1, 1, 1, 210, 105, 35, 35, 7, 7, 1, 1, 1, 1, 2310, 1155, 385, 385, 77, 77, 11, 11, 11, 11, 1, 2310, 1155, 385, 385

Offset: 1

Author

Arkadiusz Wesolowski, Nov 27 2011

Keywords

• nonn
• tabl

Comments

Row sums give A201156.

Central terms give A068111: T(2*n-1,n) = A068111(n).

T(n,1) = A034386(n).

T(n,n-1) = A089026(n) for n > 1.

T(n,n) = A000012(n).

Let n > 1 and p = A000040(n). Then T(p,p-1) = T(p+1,p-1) = p.

T(2*n-1,n-1) = A073838(n) for n > 1.

T(2*n,n+1) = A144186(n).

Examples

			1:                                   1
2:                               2       1
3:                           6       3       1
4:                       6       3       1       1
5:                   30      15      5       5       1
6:               30      15      5       5       1       1
7:           210     105     35      35      7       7       1
8:       210     105     35      35      7       7       1       1
9:   210     105     35      35      7       7       1       1       1
		

Links

• Arkadiusz Wesolowski, Rows n = 1..141 of triangle, flattened

Crossrefs

Cf. A034386.

Programs

Mathematica

lst = {}; Do[AppendTo[lst, Product[Prime[i], {i, PrimePi[n]}]/Product[Prime[i], {i, PrimePi[k]}]], {n, 12}, {k, n}]; lst (* Arkadiusz Wesolowski, Dec 02 2011 *)