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

1, 4, 2, 18, 18, 6, 6, 9, 6, 6, 150, 75, 75, 150, 30, 30, 75, 25, 75, 30, 30, 1470, 735, 1225, 1225, 735, 1470, 210, 210, 735, 245, 1225, 245, 735, 210, 210, 210, 105, 245, 245, 245, 245, 105, 210, 210, 210, 105, 35, 245, 49, 245, 35, 105, 210, 210

Offset: 1

Author

Roger L. Bagula, Apr 12 2006

Keywords

• nonn
• look
• tabl

Examples

			The triangle starts in row n=1 as:
     1;
     4,   2;
    18,  18,    6;
     6,   9,    6,    6;
   150,  75,   75,  150,  30;
    30,  75,   25,   75,  30,   30;
  1470, 735, 1225, 1225, 735, 1470, 210;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A034386.

Programs

Magma

A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;
[A034386(n)^2/(A034386(k)*A034386(n-k)): k in [1..n], n in [1..12]]; // G. C. Greubel, Jul 22 2023

Mathematica

f[n_]:= If[PrimeQ[n], n, 1];
cf[n_]:= cf[n]= If[n==0, 1, f[n]*cf[n-1]]; (* A034386 *)
T[n_, k_]:= T[n, k]= cf[n]^2/(cf[k]*cf[n-k]);
Table[T[n,k], {n, 12}, {k,n}]//Flatten

SageMath

def A034386(n): return sloane.A002110(prime_pi(n))
def T(n,k): return A034386(n)^2/(A034386(k)*A034386(n-k))
flatten([[T(n,k) for k in range(1,n+1)] for n in range(1,13)]) # G. C. Greubel, Jul 22 2023

Extensions

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