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

1,2

Links

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

Example

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;

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

Prog

(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
(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

Crossrefs

Cf. A034386.

Sequence in context: A257505 A152883 A285793 * A052966 A305135 A177248

Adjacent sequences: A117689 A117690 A117691 * A117693 A117694 A117695

Keyword

nonn,look,tabl

Author

Roger L. Bagula, Apr 12 2006

Extensions

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

Status

approved