A117693 Row sums of A117692.

1, 6, 42, 27, 480, 265, 7070, 3815, 1820, 1449, 107338, 56903, 4636632, 2635061, 993850, 633919, 71014372, 42899857, 8111619802, 4675943415, 1414861448, 819657397, 113827776894, 75106291091, 41292848428

Offset: 1

Author

Roger L. Bagula, Apr 12 2006

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A034386, A117692.

Programs

Magma

A034386:= func< n | n eq 0 select 1 else LCM(PrimesInInterval(1, n)) >;
A117692:= func< n,k | A034386(n)^2/(A034386(k)*A034386(n-k)) >;
[(&+[A117692(n,k): k in [1..n]]): n in [1..40]]; // G. C. Greubel, Jul 23 2023

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]);
a[n_]:= a[n]= Sum[T[n,k], {k,n}];
Table[a[n], {n,30}]

SageMath

def A034386(n): return sloane.A002110(prime_pi(n))
def A117692(n,k): return A034386(n)^2/(A034386(k)*A034386(n-k))
def A117693(n): return sum(A117692(n,k) for k in range(1,n+1))
[A117693(n) for n in range(1,41)] # G. C. Greubel, Jul 23 2023

Formula

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

Extensions

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