This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378133 #10 Mar 23 2025 13:55:05
%S A378133 1,2,4,6,12,24,30,60,120,210,420,840,1680,2310,4620,9240,18480,30030,
%T A378133 60060,120120,240240,480480,510510,1021020,2042040,4084080,8168160,
%U A378133 9699690,19399380,38798760,77597520,155195040,223092870,446185740,892371480,1784742960,3569485920
%N A378133 Irregular triangle T(n,k) = P(n)*2^k, n >= 0, k = 0..floor(log_2 prime(k+1)), where P = A002110.
%C A378133 Subset of A060735.
%C A378133 a(n) = min(2*a(n-1), f(a(n-1))), where f(k) is the smallest primorial (A002110) greater than k, for n > 0. - _Hal M. Switkay_, Mar 19 2025
%H A378133 Michael De Vlieger, <a href="/A378133/b378133.txt">Table of n, a(n) for n = 0..3494</a> (rows n = 0..349, flattened).
%F A378133 T(n,k) = A002110(n)*A000079(k), n >= 0, k = 0..A098388(k+1).
%F A378133 T(n,0) = A002110(n).
%F A378133 T(n,1) = A088860(n), n >= 1.
%F A378133 T(n,2) = A102476(n), n >= 2.
%F A378133 T(n,A098388(k+1)) = A378144(n).
%F A378133 Let S(n,j) = A002110(n)*j, n >= 0, j = 0..A006093(n+1) = P(n)*j, n >= 0, j = 0..prime(n+1)-1. Then T(n,k) = S(n, 2^k).
%e A378133 Rows n = 0..9:
%e A378133 n\k | 0 1 2 3 4
%e A378133 -------------------------------------------------------------
%e A378133 0 | 1 . . . .
%e A378133 1 | 2 4 . . .
%e A378133 2 | 6 12 24 . .
%e A378133 3 | 30 60 120 . .
%e A378133 4 | 210 420 840 1680 .
%e A378133 5 | 2310 4620 9240 18480 .
%e A378133 6 | 30030 60060 120120 240240 480480
%e A378133 7 | 510510 1021020 2042040 4084080 8168160
%e A378133 8 | 9699690 19399380 38798760 77597520 155195040
%e A378133 9 | 223092870 446185740 892371480 1784742960 3569485920
%t A378133 nn = 16;
%t A378133 MapIndexed[Set[P[First[#2] - 1], #1] &,
%t A378133 FoldList[Times, 1, Prime@ Range[nn + 1] ] ];
%t A378133 Union@ Flatten@
%t A378133 Table[P[i]*2^Range[0, Floor[Log2[Prime[i + 1] ] ] ], {i, 0, nn}]
%Y A378133 Cf. A000079, A002110, A060735, A088860, A098388, A102476, A378144.
%K A378133 nonn,tabf,easy
%O A378133 0,2
%A A378133 _Michael De Vlieger_, Nov 17 2024