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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 15 20:25 EDT 2024. Contains 375955 sequences. (Running on oeis4.)