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A361748 Triangle T(n, k) of distinct positive integers, n > 0, k = 1..n, read by rows and filled in the greedy way such that T(n, k) is a multiple of T(n, 1).

%I A361748 #69 Apr 03 2023 10:21:37
%S A361748 1,2,4,3,6,9,5,10,15,20,7,14,21,28,35,8,16,24,32,40,48,11,22,33,44,55,
%T A361748 66,77,12,36,60,72,84,96,108,120,13,26,39,52,65,78,91,104,117,17,34,
%U A361748 51,68,85,102,119,136,153,170,18,54,90,126,144,162,180,198,216,234,252
%N A361748 Triangle T(n, k) of distinct positive integers, n > 0, k = 1..n, read by rows and filled in the greedy way such that T(n, k) is a multiple of T(n, 1).
%C A361748 This sequence is a variant of A360371.
%C A361748 As a flat sequence, this is a permutation of the positive integers with inverse A361939.
%H A361748 Michael De Vlieger, <a href="/A361748/b361748.txt">Table of n, a(n) for n = 1..11325</a> (rows n = 1..150)
%H A361748 Rémy Sigrist, <a href="/A361748/a361748.gp.txt">PARI program</a>
%H A361748 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A361748 T(n, k) = k * T(n, 1) when T(n, 1) is a prime number.
%e A361748 Triangle T(n, k) begins:
%e A361748      1;
%e A361748      2,  4;
%e A361748      3,  6,  9;
%e A361748      5, 10, 15, 20;
%e A361748      7, 14, 21, 28, 35;
%e A361748      8, 16, 24, 32, 40,  48;
%e A361748     11, 22, 33, 44, 55,  66,  77;
%e A361748     12, 36, 60, 72, 84,  96, 108, 120;
%e A361748     13, 26, 39, 52, 65,  78,  91, 104, 117;
%e A361748     17, 34, 51, 68, 85, 102, 119, 136, 153, 170;
%e A361748     ...
%t A361748 nn = 11; c[_] = False; T[1, 1] = 1; c[1] = True; u = 2; Do[If[j == 1, k = u; m = 1, While[c[k m], m++]]; Set[{T[i, j], c[#]}, {#, True}] &[k m]; If[k == u, While[c[u], u++]], {i, 2, nn}, {j, i}]; Table[T[i, j], {i, nn}, {j, i}] // Flatten (* _Michael De Vlieger_, Apr 01 2023 *)
%o A361748 (PARI) See Links section.
%Y A361748 Cf. A360371, A361939 (inverse).
%K A361748 nonn,tabl,easy
%O A361748 1,2
%A A361748 _Rémy Sigrist_, Mar 30 2023