Problem 53029. Easy Sequences 49: Prime Little Omega Function

Created by Ramon Villamangca

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For an integer n, the prime little omega function, , is defined as the total number of distinct prime factors of n. So, if  , since , therefore .
Given an integer n, write a function that evaluates the following summation:
             
For example for :
            
In this case therefore, the function should return .
NOTE: This is an easier version of the previous problem, 'Prime Big Omega of Factorial Sequence'. So, for an added challenge, you may enjoy prime factoring each number, as the MATLAB functions 'factor', 'primes' and 'isprime' will be disabled.

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8 Solutions
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Last Solution submitted on Mar 19, 2023

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3 Comments

William on 13 Nov 2021

Ramon,
In test #7, I think the last digit of the mean(s) is maybe supposed to be a 3 rather than a 5. I'm also having some problems with test #3, but I haven't investigated that yet.

Ramon Villamangca on 14 Nov 2021

Hi William,
I can't see where our difference in test#7 is coming from, because even if I use: mean = int64(sum/numel), I'm still getting 7620740342849265. Could it be because of overflow, again? I tried not to exceed 'flintmax' this time, though. Can you publish your solution, please? Thanks.

Regarding test#3, I've checked my solution using the formula: omega(x) = numel(unique(factor(x))), and it seems correct.

William on 19 Nov 2021

Interesting. My solution fails test #7 on my laptop, but passes on the Cody server. The problem with test #3 was my fault!

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Problem 53029. Easy Sequences 49: Prime Little Omega Function

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Problem 53029. Easy Sequences 49: Prime Little Omega Function

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