A369686 LCM-transform of A359804 (see Comment and links).

1, 2, 3, 5, 2, 1, 1, 7, 3, 2, 1, 1, 11, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 7, 13, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 17, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29, 1, 1, 1, 1, 1, 1, 1, 11, 1, 5, 1, 1, 1, 1, 1, 1, 3, 31, 1

Offset

1,2

Comments

Let b(k) be the Least Common Multiple (LCM) of the first k terms of A359804, then a(n) = b(n)/b(n-1), where sequence b(n) is A369685.

The property S (as defined in A368900) refers to what is observed in the positive integers (A000027), and also in the Doudna sequence (A005940), whereby each prime power appears prior to any of its multiples. The present sequence does not have this property since, for example, 26 = a(31) precedes 13 = a(42). Thus A369804 represents a significant disturbance of A000027 in that whereas it is conjectured to be a permutation of the positive integers, it does not preserve one of the basic properties of that sequence.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Andrzej Nowicki, Strong divisibility and LCM-sequences, arXiv:1310.2416 [math.NT], 2013.

Andrzej Nowicki, Strong divisibility and LCM-sequences, Am. Math. Monthly (2015) Vol. 122, 958-966.

Formula

a(n) = A369685(n)/A369685(n-1).

Mathematica

nn = 120; c[_] = False; q[_] = 1;
Array[Set[{a[#], c[#]}, {#, True}] &, 2];
Set[{i, j}, {1, 2}]; m = 2; u = 3;
Do[
  (k = q[#]; While[c[k #], k++]; k *= #; While[c[# q[#]], q[#]++]) &[
  (p = 2; While[Divisible[i j, p], p = NextPrime[p]]; p)];
  Set[{a[n], c[k], i, j, m}, {#/m, True, j, k, #}] &[LCM[m, k]];
  If[k == u, While[c[u], u++]], {n, 3, nn}];
Array[a, nn] (* Michael De Vlieger, Jan 29 2024 *)

Crossrefs

Cf. A014963, A359804, A368900, A369685.

Sequence in context: A094122 A280185 A369060 * A082117 A269701 A011157

Adjacent sequences: A369683 A369684 A369685 * A369687 A369688 A369689

Keyword

nonn

Author

David James Sycamore, Jan 28 2024

Extensions

More terms from Michael De Vlieger, Jan 29 2024

Status

approved