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A369686
LCM-transform of A359804 (see Comment and links).
2
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Michael De Vlieger, Jan 29 2024
STATUS
approved