

A369686


LCMtransform 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
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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(n1), 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



FORMULA



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}];


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



