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

1,2

Links

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

Formula

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

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}]

Prog

(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
(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

Crossrefs

Cf. A034386, A117692.

Sequence in context: A249135 A250387 A306429 * A153243 A186885 A097253

Adjacent sequences: A117690 A117691 A117692 * A117694 A117695 A117696

Keyword

nonn,easy

Author

Roger L. Bagula, Apr 12 2006

Extensions

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

Status

approved