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A117692 Triangle T(n,k) = A034386(n)^2/(A034386(k)*A034386(n-k)), 1 <= k <= n, read by rows.

%I A117692 #10 Jul 22 2023 21:12:48
%S A117692 1,4,2,18,18,6,6,9,6,6,150,75,75,150,30,30,75,25,75,30,30,1470,735,
%T A117692 1225,1225,735,1470,210,210,735,245,1225,245,735,210,210,210,105,245,
%U A117692 245,245,245,105,210,210,210,105,35,245,49,245,35,105,210,210
%N A117692 Triangle T(n,k) = A034386(n)^2/(A034386(k)*A034386(n-k)), 1 <= k <= n, read by rows.
%H A117692 G. C. Greubel, <a href="/A117692/b117692.txt">Rows n = 1..50 of the triangle, flattened</a>
%e A117692 The triangle starts in row n=1 as:
%e A117692      1;
%e A117692      4,   2;
%e A117692     18,  18,    6;
%e A117692      6,   9,    6,    6;
%e A117692    150,  75,   75,  150,  30;
%e A117692     30,  75,   25,   75,  30,   30;
%e A117692   1470, 735, 1225, 1225, 735, 1470, 210;
%t A117692 f[n_]:= If[PrimeQ[n], n, 1];
%t A117692 cf[n_]:= cf[n]= If[n==0, 1, f[n]*cf[n-1]]; (* A034386 *)
%t A117692 T[n_, k_]:= T[n, k]= cf[n]^2/(cf[k]*cf[n-k]);
%t A117692 Table[T[n,k], {n, 12}, {k,n}]//Flatten
%o A117692 (Magma)
%o A117692 A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;
%o A117692 [A034386(n)^2/(A034386(k)*A034386(n-k)): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Jul 22 2023
%o A117692 (SageMath)
%o A117692 def A034386(n): return sloane.A002110(prime_pi(n))
%o A117692 def T(n,k): return A034386(n)^2/(A034386(k)*A034386(n-k))
%o A117692 flatten([[T(n,k) for k in range(1,n+1)] for n in range(1,13)]) # _G. C. Greubel_, Jul 22 2023
%Y A117692 Cf. A034386.
%K A117692 nonn,look,tabl
%O A117692 1,2
%A A117692 _Roger L. Bagula_, Apr 12 2006
%E A117692 Offset corrected by the Assoc. Eds. of the OEIS, Jun 27 2010