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A117692 Triangle T(n,k) = A034386(n)^2/(A034386(k)*A034386(n-k)), 1 <= k <= n, read by rows. 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
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

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Last modified June 23 16:14 EDT 2024. Contains 373651 sequences. (Running on oeis4.)