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Multiplicatively perfect numbers: Difference between revisions

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Multiplicatively perfect numbers (view source)

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<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080004080;">functioninteger</span> <span style="color: #000000;">special_numbersmultiplicatively_perfect_numbers</span> <span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n0</span><span style="color: #0000FF;">),</span>
<span style="color: #008080;">return</span> <span style="color: #7060A8000000;">productsemiprime_numbers</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n0</span><span style="color: #0000FF;">))=</span><span style="color: #000000;">n,</span>
<span style="color: #008080000000;">endfive_e_n</span> <span style="color: #0000FF;">=</span> <span style="color: #008080000000;">function5e2</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">500</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span><span style="color: #000000;">special_numbers</span><span style="color: #0000FF;">){}</span>
<span style="color: #7060A8008080;">printffor</span> <span style="color: #0000FF000000;">(n</span><span style="color: #0000000000FF;">1=</span><span style="color: #0000FF000000;">,1</span> <span style="color: #008000008080;">"%dto</span> special<span numbers under 500style="color: %s\n#000000;">5e5</span> <span style="color: #0000FF008080;">,do</span>
<span style="color: #0000FF004080;">{sequence</span> <span style="color: #7060A8000000;">lengthpn</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">joinvslice</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">shortenprime_powers</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""n</span><span style="color: #0000FF;">),</span><span style="color: #000000;">52</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">),</span><span style="color: #008000;">","</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">product</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))=</span><span style="color: #000000;">4</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">multiplicatively_perfect_numbers</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">500</span> <span style="color: #008080;">then</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">n</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">500</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d multiplicatively perfect numbers under 500: %s\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">),</span><span style="color: #008000;">","</span><span style="color: #0000FF;">)})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pn</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">semiprime_numbers</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">five_e_n</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Counts under %,7d: MPNs = %,7d Semi-primes = %,7d\n"</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">five_e_n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">multiplicatively_perfect_numbers</span><span style="color: #0000FF;">,</span><span style="color: #000000;">semiprime_numbers</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">five_e_n</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">10</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
149 specialmultiplicatively perfect numbers under 500: 6,8,10,14,15,...,482,485,489,493,497
Counts under 500: MPNs = 149 Semi-primes = 153
Counts under 5,000: MPNs = 1,353 Semi-primes = 1,365
Counts under 50,000: MPNs = 12,073 Semi-primes = 12,110
Counts under 500,000: MPNs = 108,222 Semi-primes = 108,326
</pre>
 
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