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

1,2

Comments

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

Reversal of A077011.

Links

Table of n, a(n) for n=1..36.

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).

Example

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

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 *)

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.

Sequence in context: A218969 A345291 A185973 * A051917 A302845 A291251

Adjacent sequences: A258563 A258564 A258565 * A258567 A258568 A258569

Keyword

nonn,tabl

Author

Philippe Deléham, Jun 03 2015

Status

approved