A293558 - OEIS

%I #9 Oct 29 2017 21:34:40

%S 1,3,1,15,5,2,105,35,14,8,1155,385,154,88,48,15015,5005,2002,1144,624,

%T 480,255255,85085,34034,19448,10608,8160,5760,4849845,1616615,646646,

%U 369512,201552,155040,109440,92160

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

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

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

%C 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.

%e Triangle starts:

%e n/k  1     2    3    4    5    6

%e 1    1

%e 2    3     1

%e 3    15    5    2

%e 4    105   35   14   8

%e 5    1155  385  154  88   48

%e 6    15015 5005 2002 1144 624 480

%e T(5,3) = 154: A005867(2) = 2, A002110(5) = 2310, A002110(3) = 30; 2*2310/30 = 154.

%t 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 *)

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

%K nonn,tabl

%O 1,2

%A _Bob Selcoe_, Oct 11 2017