A258566 - OEIS

%I #25 Feb 08 2024 17:39:44

%S 1,3,2,15,10,6,105,70,42,30,1155,770,462,330,210,15015,10010,6006,

%T 4290,2730,2310,255255,170170,102102,72930,46410,39270,30030,4849845,

%U 3233230,1939938,1385670,881790,746130,570570,510510

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

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

%C Reversal of A077011.

%F 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).

%e Triangle begins:

%e       1;

%e       3,     2;

%e      15,    10,    6;

%e     105,    70,   42,   30;

%e    1155,   770,  462,  330,  210;

%e   15015, 10010, 6006, 4290, 2730, 2310;

%e   ...

%p T:= n-> (m-> seq(m/ithprime(j), j=1..n))(mul(ithprime(i), i=1..n)):

%p seq(T(n), n=1..10);  # _Alois P. Heinz_, Jun 18 2015

%t T[1, 1] = 1; T[n_, n_] := T[n, n] = Prime[n-1]*T[n-1, n-1];

%t T[n_, k_] := T[n, k] = Prime[n]*T[n-1, k];

%t Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, May 26 2016 *)

%Y Row sums: A024451.

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

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

%Y For 2 <= n <= 9, T(n,2) = A118752(n-2). [corrected by _Peter Munn_, Jan 13 2018]

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

%Y Cf. A077011, A185973, A286947.

%K nonn,tabl

%O 1,2

%A _Philippe Deléham_, Jun 03 2015