Primitive Sequence

A sequence in which no term divides any other. Let S_n be the set {1,...,n}, then the number of primitive subsets of S_n are 2, 3, 5, 7, 13, 17, 33, 45, 73, 103, 205, 253, ... (OEIS A051026). For example, the five primitive sequences in S_4 are emptyset, {1}, {2}, {2,3}, {3}, {3,4}, and {4}.

See also

Nondividing Set

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Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 202, 1994.Sloane, N. J. A. Sequence A051026 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Primitive Sequence

Cite this as:

Weisstein, Eric W. "Primitive Sequence." From MathWorld--A Wolfram Web Resource.

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