Multiplicatively perfect numbers: Difference between revisions

Line 434:

five_e_n = 5e2

sequence r = {1}

for n=1 to ~~5e5~~ do

for n=1 to 5e6 do

sequence pn = vslice(prime_powers(n),2)

if product(sq_add(pn,1))=4 then

Line 448:

{length(r),join(shorten(r,"",5,"%d"),",")})

end if

printf(1,"Counts under %,7d: MPNs = %,7d Semi-primes = %,7d\n",

printf(1,"Counts under %,9d: MPNs = %,7d Semi-primes = %,7d\n",

{five_e_n,multiplicatively_perfect_numbers,semiprime_numbers})

five_e_n *= 10

Line 457:

<pre>

150 multiplicatively perfect numbers under 500: 1,6,8,10,14,...,482,485,489,493,497

Counts under 500: MPNs = 150 Semi-primes = 153

Counts under 5,000: MPNs = 1,354 Semi-primes = 1,365

Counts under 50,000: MPNs = 12,074 Semi-primes = 12,110

Counts under 500,000: MPNs = 108,223 Semi-primes = 108,326

Counts under 5,000,000: MPNs = 978,983 Semi-primes = 979,274

</pre>

@@ Line 434: / Line 434: @@
          <span style="color: #000000;">five_e_n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">5e2</span>
  <span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>
- <span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5e5</span> <span style="color: #008080;">do</span>
+ <span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5e6</span> <span style="color: #008080;">do</span>
      <span style="color: #004080;">sequence</span> <span style="color: #000000;">pn</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">prime_powers</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span><span style="color: #000000;">2</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>
@@ Line 448: / Line 448: @@
                       <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: #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: #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 %,9d: 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>
@@ Line 457: / Line 457: @@
 <pre>
 multiplicatively perfect numbers under 500: 1,6,8,10,14,...,482,485,489,493,497
-Counts under     500: MPNs =     150  Semi-primes =     153
+Counts under       500: MPNs =     150  Semi-primes =     153
-Counts under   5,000: MPNs =   1,354  Semi-primes =   1,365
+Counts under     5,000: MPNs =   1,354  Semi-primes =   1,365
-Counts under  50,000: MPNs =  12,074  Semi-primes =  12,110
+Counts under    50,000: MPNs =  12,074  Semi-primes =  12,110
-Counts under 500,000: MPNs = 108,223  Semi-primes = 108,326
+Counts under   500,000: MPNs = 108,223  Semi-primes = 108,326
+Counts under 5,000,000: MPNs = 978,983  Semi-primes = 979,274
 </pre>