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).

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, 66, 77, 12, 36, 60, 72, 84, 96, 108, 120, 13, 26, 39, 52, 65, 78, 91, 104, 117, 17, 34, 51, 68, 85, 102, 119, 136, 153, 170, 18, 54, 90, 126, 144, 162, 180, 198, 216, 234, 252

Offset

1,2

Comments

This sequence is a variant of A360371.

As a flat sequence, this is a permutation of the positive integers with inverse A361939.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows n = 1..150)

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Formula

T(n, k) = k * T(n, 1) when T(n, 1) is a prime number.

Example

Triangle T(n, k) begins:
     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,  66,  77;
    12, 36, 60, 72, 84,  96, 108, 120;
    13, 26, 39, 52, 65,  78,  91, 104, 117;
    17, 34, 51, 68, 85, 102, 119, 136, 153, 170;
    ...

Mathematica

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 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A360371, A361939 (inverse).

Sequence in context: A246278 A359299 A363473 * A377093 A372337 A371236

Adjacent sequences: A361745 A361746 A361747 * A361749 A361750 A361751

Keyword

nonn,tabl,easy

Author

Rémy Sigrist, Mar 30 2023

Status

approved