A117878 Triangle T(n,k) = A034386(n)*A049614(k) - 1 read by rows.

0, 1, 1, 5, 5, 5, 5, 5, 5, 23, 29, 29, 29, 119, 119, 29, 29, 29, 119, 119, 719, 209, 209, 209, 839, 839, 5039, 5039, 209, 209, 209, 839, 839, 5039, 5039, 40319, 209, 209, 209, 839, 839, 5039, 5039, 40319, 362879, 209, 209, 209, 839, 839, 5039, 5039, 40319, 362879

Offset

1,4

Links

G. C. Greubel, Rows n = 1..100 of the triangle, flattened

Formula

T(n, k) = A034386(n)*A049614(k) - 1.

T(n, k) = k! * A034386(n)/A034386(k) - 1 = n! * A049614(k)/A049614(n) - 1. - G. C. Greubel, Feb 06 2021

Example

The triangle starts in row n=1 as:
    0;
    1,   1;
    5,   5,   5;
    5,   5,   5,  23;
   29,  29,  29, 119, 119;
   29,  29,  29, 119, 119,  719;
  209, 209, 209, 839, 839, 5039, 5039;
  209, 209, 209, 839, 839, 5039, 5039, 40319;
  209, 209, 209, 839, 839, 5039, 5039, 40319, 362879;
  209, 209, 209, 839, 839, 5039, 5039, 40319, 362879, 3628799;

Mathematica

A034386[n_]:= Product[Prime[i], {i, PrimePi[n]}];
A049614[n_]:= n!/A034386[n];
Table[A034386[n]*A049614[k] - 1, {n, 10}, {k, n}]//Flatten (* G. C. Greubel, Feb 06 2021 *)

Prog

(Sage)
def A034386(n): return product( nth_prime(j) for j in (1..prime_pi(n)) )
def A117878(n, k): return factorial(k)*A034386(n)/A034386(k) - 1
flatten([[A117878(n, k) for k in (1..n)] for n in (1..10)]) # G. C. Greubel, Feb 06 2021

Crossrefs

Cf. A034386, A049614.

Sequence in context: A372613 A355588 A289119 * A291497 A241154 A094636

Adjacent sequences: A117875 A117876 A117877 * A117879 A117880 A117881

Keyword

nonn,tabl,less

Author

Roger L. Bagula, May 02 2006

Extensions

Index in definition and offset corrected by Assoc. Eds. of the OEIS - Jun 15 2010

Status

approved