A117693 - OEIS

%I #9 Jul 23 2023 02:13:11

%S 1,6,42,27,480,265,7070,3815,1820,1449,107338,56903,4636632,2635061,

%T 993850,633919,71014372,42899857,8111619802,4675943415,1414861448,

%U 819657397,113827776894,75106291091,41292848428

%N Row sums of A117692.

%H G. C. Greubel, <a href="/A117693/b117693.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = Sum_{k=1..n} A117692(n, k).

%t f[n_]:= If[PrimeQ[n], n, 1];

%t cf[n_]:= cf[n]= If[n==0, 1, f[n]*cf[n-1]]; (* A034386 *)

%t T[n_, k_]:= T[n,k]= cf[n]^2/(cf[k]*cf[n-k]);

%t a[n_]:= a[n]= Sum[T[n,k], {k,n}];

%t Table[a[n], {n,30}]

%o (Magma)

%o A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;

%o A117692:= func< n,k | A034386(n)^2/(A034386(k)*A034386(n-k)) >;

%o [(&+[A117692(n,k): k in [1..n]]): n in [1..40]]; // _G. C. Greubel_, Jul 23 2023

%o (SageMath)

%o def A034386(n): return sloane.A002110(prime_pi(n))

%o def A117692(n,k): return A034386(n)^2/(A034386(k)*A034386(n-k))

%o def A117693(n): return sum(A117692(n,k) for k in range(1,n+1))

%o [A117693(n) for n in range(1,41)] # _G. C. Greubel_, Jul 23 2023

%Y Cf. A034386, A117692.

%K nonn,easy

%O 1,2

%A _Roger L. Bagula_, Apr 12 2006

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