A117692 - OEIS

%I #10 Jul 22 2023 21:12:48

%S 1,4,2,18,18,6,6,9,6,6,150,75,75,150,30,30,75,25,75,30,30,1470,735,

%T 1225,1225,735,1470,210,210,735,245,1225,245,735,210,210,210,105,245,

%U 245,245,245,105,210,210,210,105,35,245,49,245,35,105,210,210

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

%H G. C. Greubel, <a href="/A117692/b117692.txt">Rows n = 1..50 of the triangle, flattened</a>

%e The triangle starts in row n=1 as:

%e      1;

%e      4,   2;

%e     18,  18,    6;

%e      6,   9,    6,    6;

%e    150,  75,   75,  150,  30;

%e     30,  75,   25,   75,  30,   30;

%e   1470, 735, 1225, 1225, 735, 1470, 210;

%t f[n_]:= If[PrimeQ[n], n, 1];

%t cf[n_]:= cf[n]= If[n==0, 1, f[n]*cf[n-1]]; (* A034386 *)

%t T[n_, k_]:= T[n, k]= cf[n]^2/(cf[k]*cf[n-k]);

%t Table[T[n,k], {n, 12}, {k,n}]//Flatten

%o (Magma)

%o A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;

%o [A034386(n)^2/(A034386(k)*A034386(n-k)): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Jul 22 2023

%o (SageMath)

%o def A034386(n): return sloane.A002110(prime_pi(n))

%o def T(n,k): return A034386(n)^2/(A034386(k)*A034386(n-k))

%o flatten([[T(n,k) for k in range(1,n+1)] for n in range(1,13)]) # _G. C. Greubel_, Jul 22 2023

%Y Cf. A034386.

%K nonn,look,tabl

%O 1,2

%A _Roger L. Bagula_, Apr 12 2006

%E Offset corrected by the Assoc. Eds. of the OEIS, Jun 27 2010