“Alladi-Grinstead Constant”的概念、定义、习题解题方法及翻译-数学辞典

单词

Alladi-Grinstead Constant

释义

Alladi-Grinstead Constant

N.B. A detailed on-line essay by S. Finchwas the starting point for this entry.

Let be the number of ways in which the Factorial can be decomposed into Factors ofthe form arranged in nondecreasing order. Also define

(1)

i.e.,

is the Least Prime Factor raised to its appropriate Power in the factorization. Then define

(2)

where

is the Natural Logarithm. For instance,












			(3)

(4)

For large

(5)

where

(6)

References

Alladi, K. and Grinstead, C. ``On the Decomposition of into Prime Powers.'' J. Number Th. 9, 452-458, 1977.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/aldgrns/aldgrns.html

Guy, R. K. ``Factorial as the Product of Large Factors.'' §B22 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 79, 1994.

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