A258566 Triangle in which n-th row contains all possible products of n-1 of the first n primes in descending order.

1, 3, 2, 15, 10, 6, 105, 70, 42, 30, 1155, 770, 462, 330, 210, 15015, 10010, 6006, 4290, 2730, 2310, 255255, 170170, 102102, 72930, 46410, 39270, 30030, 4849845, 3233230, 1939938, 1385670, 881790, 746130, 570570, 510510

Offset: 1

Author

Philippe Deléham, Jun 03 2015

Keywords

• nonn
• tabl

Comments

Triangle read by rows, truncated rows of the array in A185973.

Reversal of A077011.

Examples

			Triangle begins:
      1;
      3,     2;
     15,    10,    6;
    105,    70,   42,   30;
   1155,   770,  462,  330,  210;
  15015, 10010, 6006, 4290, 2730, 2310;
  ...
		

Crossrefs

Row sums: A024451.

T(n,1) = A070826(n).

T(n,n) = A002110(n-1).

For 2 <= n <= 9, T(n,2) = A118752(n-2). [corrected by Peter Munn, Jan 13 2018]

T(n,k) = A121281(n,k), but the latter has an extra column (0).

Cf. A077011, A185973, A286947.

Programs

Maple

T:= n-> (m-> seq(m/ithprime(j), j=1..n))(mul(ithprime(i), i=1..n)):
seq(T(n), n=1..10);  # Alois P. Heinz, Jun 18 2015

Mathematica

T[1, 1] = 1; T[n_, n_] := T[n, n] = Prime[n-1]*T[n-1, n-1];
T[n_, k_] := T[n, k] = Prime[n]*T[n-1, k];
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, May 26 2016 *)

Formula

T(1,1) = 1, T(n,k) = A000040(n)*T(n-1,k) for k < n, T(n,n) = A000040(n-1) * T(n-1,n-1).