A343012 Lexicographically earliest sequence of distinct numbers whose partial products have mutually distinct exponents in their prime factorization (A130091).

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

Offset

1,2

Comments

Is this sequence a permutation of the positive integers?

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

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

Crossrefs

Cf. A130091, A343013.

Sequence in context: A234519 A289726 A308598 * A143692 A337116 A338618

Adjacent sequences: A343009 A343010 A343011 * A343013 A343014 A343015

Keyword

nonn,look

Author

Amiram Eldar, Apr 02 2021

Status

approved