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 A339491 Lexicographically earliest longest simple path in the divisor graph of {1,...,n}. Irregular triangle read by rows. 6
 1, 1, 2, 2, 1, 3, 2, 4, 1, 3, 2, 4, 1, 3, 3, 6, 2, 4, 1, 5, 3, 6, 2, 4, 1, 5, 3, 6, 2, 4, 8, 1, 5, 4, 8, 2, 6, 3, 9, 1, 5, 4, 8, 1, 5, 10, 2, 6, 3, 9, 4, 8, 1, 5, 10, 2, 6, 3, 9, 5, 10, 2, 8, 4, 12, 6, 3, 9, 1, 7, 5, 10, 2, 8, 4, 12, 6, 3, 9, 1, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A simple path in the divisor graph of {1,...,n} is a sequence of distinct numbers between 1 and n such that if k immediately follows m, then either k divides m or m divides k. For more information, references and links see A337125. LINKS EXAMPLE 1:                     [1], 2:                    [1, 2], 3:                  [2, 1, 3], 4:                 [2, 4, 1, 3], 5:                 [2, 4, 1, 3], 6:              [3, 6, 2, 4, 1, 5], 7:              [3, 6, 2, 4, 1, 5], 8:             [3, 6, 2, 4, 8, 1, 5], 9:            [4, 8, 2, 6, 3, 9, 1, 5], 10:         [4, 8, 1, 5, 10, 2, 6, 3, 9], 11:         [4, 8, 1, 5, 10, 2, 6, 3, 9], 12:      [5, 10, 2, 8, 4, 12, 6, 3, 9, 1, 7], 13:      [5, 10, 2, 8, 4, 12, 6, 3, 9, 1, 7], 14:     [5, 10, 1, 7, 14, 2, 8, 4, 12, 6, 3, 9], 15:   [6, 12, 4, 8, 1, 7, 14, 2, 10, 5, 15, 3, 9], 16:  [6, 12, 4, 8, 16, 1, 7, 14, 2, 10, 5, 15, 3, 9]. MAPLE with(Iterator): DivisorPath := proc(n, k) local c, p, w, isok;     isok := proc(A) local e, i, di; e := nops(A) - 1;        di := (n, k) -> evalb(irem(n, k) = 0 or irem(k, n) = 0):        for i from 1 to e while di(A[i], A[i+1]) do od;        return evalb(i = e + 1) end:     for c in Combination(n, k) do        for p in Permute([seq(j + 1, j in c)], k) do            w := convert(p, list);            if isok(w) then return w fi: od  od  end: A337125 := [1, 2, 3, 4, 4, 6, 6, 7, 8, 9, 9]: for n from 1 to 9 do DivisorPath(n, A337125[n]) od; CROSSREFS Cf. A337125 (row length), A339490. Cf. A339492, A339489, A339496. Cf. A340114 (a variant problem). Sequence in context: A159803 A308934 A058741 * A291712 A074945 A323479 Adjacent sequences:  A339488 A339489 A339490 * A339492 A339493 A339494 KEYWORD nonn,tabf AUTHOR Peter Luschny, Dec 29 2020 EXTENSIONS Signposting added to first comment by Peter Munn, Mar 12 2021 STATUS approved

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)