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Primitive Sequence

المؤلف:  Guy, R. K.

المصدر:  Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag

الجزء والصفحة:  ...

3-11-2020

1721

Primitive Sequence

A sequence in which no term divides any other. Let  be the set {1,...,n}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline2.gif" style="height:15px; width:54px" />, then the number of primitive subsets of  are 2, 3, 5, 7, 13, 17, 33, 45, 73, 103, 205, 253, ... (OEIS A051026). For example, the five primitive sequences in  are , {1}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline6.gif" style="height:15px; width:17px" />, {2}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline7.gif" style="height:15px; width:17px" />, {2,3}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline8.gif" style="height:15px; width:32px" />, {3}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline9.gif" style="height:15px; width:17px" />, {3,4}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline10.gif" style="height:15px; width:32px" />, and {4}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline11.gif" style="height:15px; width:17px" />.

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REFERENCES:

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."