prime factor

(redirected from Prime divisor)
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Related to Prime divisor: Prime number theory
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the prime factors of a quantity are all of the prime quantities that will exactly divide the given quantity

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The problem is to write a program which finds the smallest prime divisor of an integer N > 1.
We refer to this method as the prime divisor coloring.
Let p be the largest prime divisor of |H| and let P be a Sylow p-subgroup of H.
Writing this fact for all prime divisors of a, we get a|b.
Note that F(n) is a complete additive function, and if n [member of] A with n = pk , then S(n) = S(p) = p, and any prime divisor q of k satisfying q [less than or equal to] [n.
n], there exists at least one prime divisor pi such that [p.
It is easy to prove that for each prime p one has P(p) = p, and if n is a square-free number, then P(n) = greatest prime divisor of n.
Put w(n) = number of distinct prime divisors of n, where n > 1.
Put [omega](n) = number of distinct prime divisors of n, where n > 1.
r), then we have SP(n) = U(n), where U(n) = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the product over all different prime divisors of n.
But for most n, we have [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denotes the product over all different prime divisors of n.
kappa]] (n)), and give a sharper asymptotic formula for it, where [OMEGA](n) denotes the number of all prime divisors of n.
If n has more than two prime divisors, from the properties of Smarandache function S(n) we know that