A117684 Row sums of A117683.

1, 2, 3, 13, 11, 49, 27, 141, 523, 3081, 923, 5509, 1371, 7617, 24391, 84933, 14795, 110329, 20859, 142101, 499843, 1858209, 241211, 2312077, 8417451, 70482153, 251680159, 935093181, 95916299, 1102272481, 131510523, 1270525629, 4572551611, 17189356473

Offset: 1

Author

Roger L. Bagula, Apr 12 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A117683.

Programs

Magma

A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;
[(&+[Binomial(n,k)*A034386(k)*A034386(n-k)/A034386(n): k in [1..n]]): n in [1..40]]; // G. C. Greubel, Jul 21 2023

Mathematica

f[n_]:= If[PrimeQ[n], 1, n];
cf[n_]:= cf[n]= If[n==0, 1, f[n]*cf[n-1]]; (* A049614 *)
T[n_, k_]:= T[n, k]= cf[n]/(cf[k]*cf[n-k]);
a[n_]:= a[n]= Sum[T[n,k], {k,n}];
Table[a[n], {n,40}]

SageMath

@CachedFunction
def A034386(n): return product(nth_prime(j) for j in range(1, 1+prime_pi(n)))
def A117684(n): return sum(binomial(n,k)*A034386(k)*A034386(n-k)/A034386(n) for k in range(1,n+1))
[A117684(n) for n in range(1,41)] # G. C. Greubel, Jul 21 2023

Formula

a(n) = Sum_{k=1..n} A117683(n,k).

Extensions

Description simplified, offset corrected by the Assoc. Eds. of the OEIS, Jun 27 2010