A293558 Triangle T(n,k) read by rows: T(n,k) = A005867(k-1)*A002110(n)/A002110(k).

1, 3, 1, 15, 5, 2, 105, 35, 14, 8, 1155, 385, 154, 88, 48, 15015, 5005, 2002, 1144, 624, 480, 255255, 85085, 34034, 19448, 10608, 8160, 5760, 4849845, 1616615, 646646, 369512, 201552, 155040, 109440, 92160

Offset: 1

Author

Bob Selcoe, Oct 11 2017

Keywords

• nonn
• tabl

Comments

T(n,k) is the triangle in A174909 with reversed row order. (See that sequence for additional comments).

Row sums = A053144(n) = A002110(n) - T(n+1,n+1).

T(n,k) = number of terms with smallest prime factor prime(k) contained in primorial(n) consecutive numbers, k <= n. For example, T(5,4) = 88, so there are 88 terms with smallest prime factor 7 in any sequence of 2310 consecutive numbers.

Examples

			Triangle starts:
n/k  1     2    3    4    5    6
1    1
2    3     1
3    15    5    2
4    105   35   14   8
5    1155  385  154  88   48
6    15015 5005 2002 1144 624 480
T(5,3) = 154: A005867(2) = 2, A002110(5) = 2310, A002110(3) = 30; 2*2310/30 = 154.
		

Crossrefs

Cf. A000040 (prime numbers), A002110, A005867, A053144, A174909 (this triangle with reversed row order).

Programs

Mathematica

Table[#1 Product[EulerPhi@ Prime@ i, {i, k - 1}]/#2 & @@ Map[Product[ Prime@ i, {i, #}] &, {n, k}], {n, 8}, {k, n}] // Flatten (* Michael De Vlieger, Oct 12 2017 *)