“Least Prime Factor”的概念、定义、习题解题方法及翻译-数学辞典

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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