Achilles numbers: Difference between revisions

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Based on Wikipedia definition: n = p<sub>1</sub><sup>a<sub>1</sub></sup>p<sub>2</sub><sup>a<sub>2</sub></sup>…p<sub>k</sub><sup>a<sub>k</sub></sup> is an Achilles number if min(a<sub>1</sub>, a<sub>2</sub>, …, a<sub>k</sub>) ≥ 2 and gcd(a<sub>1</sub>, a<sub>2</sub>, …, a<sub>k</sub>) = 1.
Based on Wikipedia definition: n = p<sub>1</sub><sup>a<sub>1</sub></sup>p<sub>2</sub><sup>a<sub>2</sub></sup>…p<sub>k</sub><sup>a<sub>k</sub></sup> is an Achilles number if min(a<sub>1</sub>, a<sub>2</sub>, …, a<sub>k</sub>) ≥ 2 and gcd(a<sub>1</sub>, a<sub>2</sub>, …, a<sub>k</sub>) = 1.
{{works with|HP|49g}}
{{works with|HP|49g}}
≪ → s
≪ FACTORS
⚫
'''IF''' DUP SIZE 4 < '''THEN''' DROP 0
≪ { } DUP
⚫
1 s SIZE '''FOR''' j
⚫
SWAP s j GET + '''NEXT'''
≫ ≫ '<span style="color:blue">UNBUNDL</span>' STO
≪ DUP FACTORS
⚫
'''IF''' DUP SIZE 4 < '''THEN''' DROP2 0
'''ELSE'''
'''ELSE'''
<span style="color:blue">UNBUNDL</span> → p a <span style="color:grey">@ separates prime factors from their exponents</span>
{ } 2 3 PICK SIZE '''FOR''' j <span style="color:grey">@ keeps exponents only</span>
⚫
OVER j GET +
≪ 1 p INV - ΠLIST →NUM * <span style="color:grey">@ get phi(n)</span>
⚫
2 '''STEP''' NIP
⚫
a ≪ MIN ≫ STREAM 2 ≥
a ≪ GCD ≫ STREAM 1 ==
→ a
⚫
≪ a ≪ MIN ≫ STREAM 2 ≥ a ≪ GCD ≫ STREAM 1 == AND
AND * <span style="color:grey">@ if Achilles, returns phi(n))</span>
≫
≫
'''END'''
'''END'''
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≪ { } 1 → n
≪ { } 1 → n
≪ '''WHILE''' DUP SIZE 20 < '''REPEAT'''
≪ '''WHILE''' DUP SIZE 20 < '''REPEAT'''
'''IF''' 'n' INCR <span style="color:blue">ACH?</span> 4 RND R→I <span style="color:blue">ACH?</span> '''THEN''' n + '''END'''
'''IF''' 'n' INCR <span style="color:blue">ACH?</span>
'''THEN''' IF n EULER <span style="color:blue">ACH?</span> '''THEN''' n + '''END END'''
'''END'''
'''END'''
≫ ≫ EVAL
≫ ≫ EVAL
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1: {500 864 1944 2000 2592 3456 5000 10125 10368 12348 12500 16875 19652 19773 30375 31104 32000 33275 37044 40500}
1: {500 864 1944 2000 2592 3456 5000 10125 10368 12348 12500 16875 19652 19773 30375 31104 32000 33275 37044 40500}
</pre>
</pre>
First 50 Achilles numbers found in 1 minutes 53 seconds on the ''iHP48'' emulator running on a iPhone Xr; first 20 strong Achilles numbers found in 14 minutes on the same platform.
First 50 Achilles numbers found in 53 seconds on the ''iHP48'' emulator running on a iPhone Xr; first 20 strong Achilles numbers found in 5 minutes 13 seconds on the same platform.


=={{header|Rust}}==
=={{header|Rust}}==
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