A117878 - OEIS

%I #12 Feb 06 2021 07:44:46

%S 0,1,1,5,5,5,5,5,5,23,29,29,29,119,119,29,29,29,119,119,719,209,209,

%T 209,839,839,5039,5039,209,209,209,839,839,5039,5039,40319,209,209,

%U 209,839,839,5039,5039,40319,362879,209,209,209,839,839,5039,5039,40319,362879

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

%H G. C. Greubel, <a href="/A117878/b117878.txt">Rows n = 1..100 of the triangle, flattened</a>

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

%F T(n, k) = k! * A034386(n)/A034386(k) - 1 = n! * A049614(k)/A049614(n) - 1. - _G. C. Greubel_, Feb 06 2021

%e The triangle starts in row n=1 as:

%e     0;

%e     1,   1;

%e     5,   5,   5;

%e     5,   5,   5,  23;

%e    29,  29,  29, 119, 119;

%e    29,  29,  29, 119, 119,  719;

%e   209, 209, 209, 839, 839, 5039, 5039;

%e   209, 209, 209, 839, 839, 5039, 5039, 40319;

%e   209, 209, 209, 839, 839, 5039, 5039, 40319, 362879;

%e   209, 209, 209, 839, 839, 5039, 5039, 40319, 362879, 3628799;

%t A034386[n_]:= Product[Prime[i], {i, PrimePi[n]}];

%t A049614[n_]:= n!/A034386[n];

%t Table[A034386[n]*A049614[k] - 1, {n, 10}, {k, n}]//Flatten (* _G. C. Greubel_, Feb 06 2021 *)

%o (Sage)

%o def A034386(n): return product( nth_prime(j) for j in (1..prime_pi(n)) )

%o def A117878(n, k): return factorial(k)*A034386(n)/A034386(k) - 1

%o flatten([[A117878(n,k) for k in (1..n)] for n in (1..10)]) # _G. C. Greubel_, Feb 06 2021

%Y Cf. A034386, A049614.

%K nonn,tabl,less

%O 1,4

%A _Roger L. Bagula_, May 02 2006

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