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A117684 Row sums of A117683.

%I A117684 #7 Jul 22 2023 12:11:09
%S A117684 1,2,3,13,11,49,27,141,523,3081,923,5509,1371,7617,24391,84933,14795,
%T A117684 110329,20859,142101,499843,1858209,241211,2312077,8417451,70482153,
%U A117684 251680159,935093181,95916299,1102272481,131510523,1270525629,4572551611,17189356473
%N A117684 Row sums of A117683.
%H A117684 G. C. Greubel, <a href="/A117684/b117684.txt">Table of n, a(n) for n = 1..1000</a>
%F A117684 a(n) = Sum_{k=1..n} A117683(n,k).
%t A117684 f[n_]:= If[PrimeQ[n], 1, n];
%t A117684 cf[n_]:= cf[n]= If[n==0, 1, f[n]*cf[n-1]]; (* A049614 *)
%t A117684 T[n_, k_]:= T[n, k]= cf[n]/(cf[k]*cf[n-k]);
%t A117684 a[n_]:= a[n]= Sum[T[n,k], {k,n}];
%t A117684 Table[a[n], {n,40}]
%o A117684 (Magma)
%o A117684 A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;
%o A117684 [(&+[Binomial(n,k)*A034386(k)*A034386(n-k)/A034386(n): k in [1..n]]): n in [1..40]]; // _G. C. Greubel_, Jul 21 2023
%o A117684 (SageMath)
%o A117684 @CachedFunction
%o A117684 def A034386(n): return product(nth_prime(j) for j in range(1, 1+prime_pi(n)))
%o A117684 def A117684(n): return sum(binomial(n,k)*A034386(k)*A034386(n-k)/A034386(n) for k in range(1,n+1))
%o A117684 [A117684(n) for n in range(1,41)] # _G. C. Greubel_, Jul 21 2023
%Y A117684 Cf. A117683.
%K A117684 nonn
%O A117684 1,2
%A A117684 _Roger L. Bagula_, Apr 12 2006
%E A117684 Description simplified, offset corrected by the Assoc. Eds. of the OEIS, Jun 27 2010