login
Triangle read by rows: T(n,k) = (k+1)*A028815(n) for 0 <= k <= n.
1

%I #53 Aug 05 2024 08:40:29

%S 2,3,6,4,8,12,6,12,18,24,8,16,24,32,40,12,24,36,48,60,72,14,28,42,56,

%T 70,84,98,18,36,54,72,90,108,126,144,20,40,60,80,100,120,140,160,180,

%U 24,48,72,96,120,144,168,192,216,240,30,60,90,120,150,180,210,240,270,300,330

%N Triangle read by rows: T(n,k) = (k+1)*A028815(n) for 0 <= k <= n.

%H G. C. Greubel, <a href="/A289055/b289055.txt">Rows n = 0..50 of the triangle, flattened</a>

%F a(n) = A289108(n) + 1.

%e Triangle begins:

%e 2;

%e 3, 6;

%e 4, 8, 12;

%e 6, 12, 18, 24;

%e 8, 16, 24, 32, 40;

%e 12, 24, 36, 48, 60, 72;

%e 14, 28, 42, 56, 70, 84, 98;

%e 18, 36, 54, 72, 90, 108, 126, 144;

%e 20, 40, 60, 80, 100, 120, 140, 160, 180;

%e ...

%t Join[{2}, t[n_, k_] := (k + 1) (Prime[n] + 1); Table[t[n, k], {n, 10}, {k, 0, n}] //Flatten]

%o (Magma) /* As triangle (here NthPrime(0)=1) */ [[(k+1)*(NthPrime(n)+1): k in [0..n]]: n in [0.. 15]];

%o (SageMath)

%o def A289055(n,k): return 2 if n==0 else (k+1)*(nth_prime(n) +1)

%o flatten([[A289055(n,k) for k in range(n+1)] for n in range(13)]) # _G. C. Greubel_, Aug 05 2024

%Y Cf. A289108.

%Y Columns k: A028815 (k=0), A089241 (k=1), A247159 (k=2), A273801 (k=3).

%K nonn,tabl,less

%O 0,1

%A _Vincenzo Librandi_, Sep 02 2017