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Good Binomial Coefficient

A good binomial coefficient is a binomial coefficient (N; k) with k>=2 whose least prime factor satisfies

lpf(N; k)>k

(Erdős et al. 1993). This is equivalent to the requirement that

GCD((N; k),k!)=1.

The first few good binomial coefficients are therefore (3; 2), (5; 4), (6; 2), (7; 2), (7; 3), (7; 4), (7; 6), (10; 2), .... Good binomial coefficients are closely related to the Erdős-selfridge function g(k), which gives the least integer N>k+1 such that (N; k) is good.

See also

Binomial Coefficient, Deficiency, Erdős-Selfridge Function, Exceptional Binomial Coefficient

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References

Erdős, P.; Lacampagne, C. B.; and Selfridge, J. L. "Estimates of the Least Prime Factor of a Binomial Coefficient." Math. Comput. 61, 215-224, 1993.

Referenced on Wolfram|Alpha

Good Binomial Coefficient

Cite this as:

Weisstein, Eric W. "Good Binomial Coefficient." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GoodBinomialCoefficient.html

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