Primitive Sequence
المؤلف:
Guy, R. K.
المصدر:
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag
الجزء والصفحة:
...
3-11-2020
1177
Primitive Sequence
A sequence in which no term divides any other. Let 
be the set ![<span style=]()
{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 
, ![<span style=]()
{1}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline6.gif" style="height:15px; width:17px" />, ![<span style=]()
{2}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline7.gif" style="height:15px; width:17px" />, ![<span style=]()
{2,3}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline8.gif" style="height:15px; width:32px" />, ![<span style=]()
{3}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline9.gif" style="height:15px; width:17px" />, ![<span style=]()
{3,4}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline10.gif" style="height:15px; width:32px" />, and ![<span style=]()
{4}" src="https://mathworld.wolfram.com/images/equations/PrimitiveSequence/Inline11.gif" style="height:15px; width:17px" />.
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."
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