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A117693 Row sums of A117692.

%I A117693 #9 Jul 23 2023 02:13:11
%S A117693 1,6,42,27,480,265,7070,3815,1820,1449,107338,56903,4636632,2635061,
%T A117693 993850,633919,71014372,42899857,8111619802,4675943415,1414861448,
%U A117693 819657397,113827776894,75106291091,41292848428
%N A117693 Row sums of A117692.
%H A117693 G. C. Greubel, <a href="/A117693/b117693.txt">Table of n, a(n) for n = 1..1000</a>
%F A117693 a(n) = Sum_{k=1..n} A117692(n, k).
%t A117693 f[n_]:= If[PrimeQ[n], n, 1];
%t A117693 cf[n_]:= cf[n]= If[n==0, 1, f[n]*cf[n-1]]; (* A034386 *)
%t A117693 T[n_, k_]:= T[n,k]= cf[n]^2/(cf[k]*cf[n-k]);
%t A117693 a[n_]:= a[n]= Sum[T[n,k], {k,n}];
%t A117693 Table[a[n], {n,30}]
%o A117693 (Magma)
%o A117693 A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;
%o A117693 A117692:= func< n,k | A034386(n)^2/(A034386(k)*A034386(n-k)) >;
%o A117693 [(&+[A117692(n,k): k in [1..n]]): n in [1..40]]; // _G. C. Greubel_, Jul 23 2023
%o A117693 (SageMath)
%o A117693 def A034386(n): return sloane.A002110(prime_pi(n))
%o A117693 def A117692(n,k): return A034386(n)^2/(A034386(k)*A034386(n-k))
%o A117693 def A117693(n): return sum(A117692(n,k) for k in range(1,n+1))
%o A117693 [A117693(n) for n in range(1,41)] # _G. C. Greubel_, Jul 23 2023
%Y A117693 Cf. A034386, A117692.
%K A117693 nonn,easy
%O A117693 1,2
%A A117693 _Roger L. Bagula_, Apr 12 2006
%E A117693 Description simplified, offset corrected by the Assoc. Eds. of the OEIS, Jun 27 2010