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单词 Least Prime Factor
释义

Least Prime Factor

For an Integer , let denote the Least Prime Factor of , i.e., the number inthe factorization


with for . For , 3, ..., the first few are 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 2, 3, ...(Sloane's A020639). The above plot of the least prime factor function can be seen to resemble a jagged terrain of mountains,which leads to the appellation of ``Twin Peaks'' to a Pair of Integers such that
1. ,

2. ,

3. For all , Implies .
The least multiple prime factors for Squareful integers are 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 2,... (Sloane's A046027).

See also Alladi-Grinstead Constant, Distinct Prime Factors, Erdös-SelfridgeFunction, Factor, Greatest Prime Factor, Least Common Multiple, Mangoldt Function,Prime Factors, Twin Peaks


References

Sloane, N. J. A.A020639 andA046027 in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html.


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