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 A287691 #12 Jun 07 2017 19:20:09
%S A287691 1,2,1,2,4,1,3,7,8,1,5,12,23,17,1,6,16,44,56,29,1,9,24,78,130,139,41,
%T A287691 1,9,30,107,214,351,224,59,1,11,39,154,332,707,650,389,76,1,17,64,261,
%U A287691 598,1475,1637,1489,640,112,1,21,82,378,902,2496,3155,3782
%N A287691 Triangle read by rows: T(n,k) (0 <= k <= n) is the number of squarefree numbers A002110(n) <= m <= (A002110(n+1)-1) such that A001221(m) = n and m is divisible by A002110(k).
%C A287691 Let p_n# = A002110(n).
%C A287691 T(n,n) = 1 since p_n# is the only primorial divisible by p_n#.
%C A287691 Maxima for the first rows are {1, 2, 4, 8, 23, 56, 139, 351, 707, 1637, 3782, 8843, 18442, 38103, 77355, 177358, 387470, ...} at positions {1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 7, 7, 7, 9, 10, 10, 10, ...}.
%C A287691 A287484(n) = sum of row n. - _Michael De Vlieger_, Jun 07 2017
%H A287691 Michael De Vlieger, <a href="/A287691/b287691.txt">Table of n, a(n) for n = 0..230</a> (rows 0 <= n <= 20).
%e A287691 The triangle starts:
%e A287691 n | 0 1 2 3 4 5 6 7 8 9 10
%e A287691 -------------------------------------------------------------
%e A287691 0 | 1
%e A287691 1 | 2 1
%e A287691 2 | 2 4 1
%e A287691 3 | 3 7 8 1
%e A287691 4 | 5 12 23 17 1
%e A287691 5 | 6 16 44 56 29 1
%e A287691 6 | 9 24 78 130 139 41 1
%e A287691 7 | 9 30 107 214 351 224 59 1
%e A287691 8 | 11 39 154 332 707 650 389 76 1
%e A287691 9 | 17 64 261 598 1475 1637 1489 640 112 1
%e A287691 10 | 21 82 378 902 2496 3155 3782 2505 1041 144 1
%e A287691 ...
%e A287691 Let p_n# = A002110(n).
%e A287691 There are A287484(2) = 7 squarefree numbers m between p_2# = 6 and p_3# - 1 = 29: {6, 10, 14, 15, 21, 22, 26}. Of these, {15, 21} are divisible by p_0# = 1, {10, 14, 22, 26} are divisible by p_1# = 2, and {6} is divisible by p_2# = 6. Thus, T(2,k) = {2, 4, 1}.
%e A287691 Note that the terms {15, 21}, {10, 14, 22, 26}, and {6} pertaining to the above example appear in row n of A287483 sorted as {6, 10, 14, 15, 21, 22, 26}. - _Michael De Vlieger_, Jun 07 2017
%t A287691 Table[Length /@ Split@ Sort@ Map[Block[{k = 1}, While[Divisible[#, Prime@ k], k++]; k] &, Select[Range[#, Prime[n + 1] #], And[SquareFreeQ@ #, PrimeOmega@ # == n] &] &@ Product[Prime@ i, {i, n}]], {n, 0, 6}] // Flatten (* _Michael De Vlieger_, May 29 2017 *)
%Y A287691 Cf. A001221, A002110, A287483, A287484.
%K A287691 nonn,tabl
%O A287691 0,2
%A A287691 _Michael De Vlieger_, May 29 2017