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A343012
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Lexicographically earliest sequence of distinct numbers whose partial products have mutually distinct exponents in their prime factorization (A130091).
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3
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1, 2, 4, 3, 6, 5, 8, 9, 10, 7, 12, 15, 14, 11, 16, 18, 20, 21, 22, 13, 24, 25, 27, 28, 30, 32, 33, 26, 17, 35, 36, 40, 42, 44, 39, 34, 19, 45, 48, 49, 50, 54, 55, 52, 51, 38, 23, 56, 60, 63, 64, 66, 65, 68, 57, 46, 29, 70, 72, 75, 77, 78, 80, 81, 84, 85, 76, 69
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OFFSET
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1,2
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COMMENTS
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Is this sequence a permutation of the positive integers?
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LINKS
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EXAMPLE
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The first partial products are:
1
1 * 2 = 2 = 2^1
1 * 2 * 4 = 8 = 2^3
1 * 2 * 4 * 3 = 24 = 2^3 * 3^1
1 * 2 * 4 * 3 * 6 = 144 = 2^4 * 3^2
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MATHEMATICA
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q[n_] := UnsameQ @@ FactorInteger[n][[;; , 2]]; seq = {1}; prod = 1; Do[k = 1; While[MemberQ[seq, k] || ! q[k*prod], k++]; AppendTo[seq, k]; prod *= k, {100}]; seq
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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