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Primitive Sequence


A primitive sequence is a sequence of positive integers in which no term divides any other. Let S_n be the set {1,...,n}, where n is a positive integer. The numbers of primitive subsets of S_n for n=1, 2, ... are 2, 3, 5, 7, 13, 17, 33, 45, 73, 103, 205, 253, ... (OEIS A051026). For example, the seven primitive subsets of S_4 are emptyset, {1}, {2}, {2,3}, {3}, {3,4}, and {4}.

For primitive sets A of integers greater than 1, the Erdős primitive set conjecture concerns maximizing the weighted sum sum_(a in A)1/(alna).


See also

Nondividing Set

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References

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 202, 1994.Numberphile. "Primes and Primitive Sets (an Erdős Conjecture Is Cracked)." Jun. 16, 2022. https://www.youtube.com/watch?v=33YSWaR3kAQ.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 Resource. https://mathworld.wolfram.com/PrimitiveSequence.html

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