2 июн. 2013 г. · This formula says that if n is a large number, we can estimate the distribution of the number of prime factors for numbers of this range. For ...

19 апр. 2020 г. · There doesn't seem to be a direct formula for the sum of distinct prime factors of n. If n is prime the answer is n itself.

1 июл. 2016 г. · It is a computable function: there exists an exponential-time algorithm, eg, factorize the number with trial division, then count the number of distinct ...

1 мар. 2021 г. · Using common notation, ω(n) is the number of distinct prime factors on n. Similiarly, Ω(n) is the number of prime factors of ...

2 апр. 2015 г. · The standard definition of ω(n) is the number of distinct prime divisors of n; see here. Note also that it must be distinct instead of with multiplicity.

26 авг. 2017 г. · Therefore, the number of general factors of a number,given that the number has n distinct prime factors, is equal to: [C(n,1)+C(n,2)+C(n,3)+...+ ...

3 мар. 2020 г. · A related result, often called the Selberg–Sathe theorem, actually gives the asymptotic formula #{n≤x:ω(n)=k}∼xlogx(loglogx)k−1(k−1)!. In ...

16 мая 2015 г. · Let n=pe11pe22⋯pekk an integer with pi prime and ei∈N. The prime factorization can assumed to be known, i.e., we already know p1,…

22 сент. 2019 г. · logPN=N∑k=1logpk.

19 мая 2018 г. · Let πk(n) be the number of integers ≤n with exactly k distinct prime factors. You are looking for ∑∞m=1πm2(n)=π(n)+π4(n)+π9(n)+…