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

Author

Amiram Eldar, Apr 02 2021

Keywords

• nonn
• look

Comments

Is this sequence a permutation of the positive integers?

Examples

			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
		

Links

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

Crossrefs

Cf. A130091, A343013.

Programs

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