The Weekly Challenge

09. TASK #1: Brilliant Numbers

HEADLINES

Welcome to a very special Week #169.

Why so special?

Well, we got two new members joining the Team PWC, Stephen G Lynn and habere-et-dispertire.

There is another reason why it is so special. Thanks to the kind help by Lance Wicks, we finally have the design ready for the 1000 days celebration T-shirt. It is time to finalise the list of champions. I am hoping by next week, I will have the final list. Following that, I will place the order. Sincere apology for the delay.

I missed the deadline to participate last week again. I find it hard to be regular. Talking about regular contributors, Laurent Rosenfeld is one of few who hardly missed a week. No wonder he is currently rank #1 as of today.

Welcome back Bruce Gray and Humberto Massa after a short break.

Good luck for the next challenge.

Blogs with Creative Title

1. Take the Long Way Home by Adam Russell.

2. Primarily Prime by Arne Sommer.

3. This Is Gonna Take FOREVER! by Dave Jacoby.

4. prime numbers in many ways! by Luca Ferrari.

5. More funny numbers … and a very big one by Peter Campbell Smith.

6. At Home with the Perrins by Roger Bell_West.

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2. Pull Requests: 6,247 (+46)

3. Contributors: 197 (+1)

4. Fork: 250 (+1)

5. Stars: 138 (+3)

Our solo sponsor Pete Sergeant has been a great support to keep us motivated. We are lucky that he agreed to continue the journey with us in the year 2022. I would like to personally thank Pete and his entire team for their generosity. It would be great if we could add few more to sponsor the prize money so that we could go back and declare weekly champions as we have done in the past. I hope and wish this will become possible in 2022. The amount doesn’t have to be huge. However, it would be nice to show off bunch of supporters. If an organisation comes forward and supports us then that would be the ultimate achievement.

RECAP

Quick recap of The Weekly Challenge - 168 by Mohammad S Anwar.

PERL REVIEW

Please check out Perl solutions review of The Weekly Challenge - 162 by Colin Crain.

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RAKU REVIEW

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CHART

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I would like to THANK every member of the team for their valuable suggestions. Please do share your experience with us.

NEW MEMBERS

1. Stephen G Lynn, an expert `Perl`/`Raku` hacker.

2. habere-et-dispertire, an expert `Raku` hacker.

Please find out How to contribute?, if you have any doubts.

Please try the excellent tool EZPWC created by respected member Saif Ahmed of Team PWC.

GUESTS

Please checkout the guest contributions for the Week #168.

Please find past solutions by respected guests. Please share your creative solutions in other languages.

Task 1: Brilliant Numbers

Submitted by: Mohammad S Anwar

Write a script to generate first 20 Brilliant Numbers.

Brilliant numbers are numbers with two prime factors of the same length.

The number should have exactly two prime factors, i.e. it’s the product of two primes of the same length.

For example,

24287 = 149 x 163
24289 = 107 x 227

Therefore 24287 and 24289 are 2-brilliant numbers.
These two brilliant numbers happen to be consecutive as there are no even brilliant numbers greater than 14.

Output

4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 121, 143, 169, 187, 209, 221, 247, 253, 289, 299

Task 2: Achilles Numbers

Submitted by: Mohammad S Anwar

Write a script to generate first 20 Achilles Numbers. Please checkout wikipedia for more information.

An Achilles number is a number that is powerful but imperfect (not a perfect power). Named after Achilles, a hero of the Trojan war, who was also powerful but imperfect.

A positive integer n is a powerful number if, for every prime factor p of n, p^2 is also a divisor.

A number is a perfect power if it has any integer roots (square root, cube root, etc.).

For example 36 factors to (2, 2, 3, 3) - every prime factor (2, 3) also has its square as a divisor (4, 9). But 36 has an integer square root, 6, so the number is a perfect power.

But 72 factors to (2, 2, 2, 3, 3); it similarly has 4 and 9 as divisors, but it has no integer roots. This is an Achilles number.

Output

 72, 108,  200,  288,  392,  432,  500,  648,  675,  800,  864, 968, 972, 1125, 1152, 1323, 1352, 1372, 1568, 1800

Last date to submit the solution 23:59 (UK Time) Sunday 19th June 2022.