Multiplicatively perfect numbers: Difference between revisions
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{{libheader|Wren-math}} |
{{libheader|Wren-math}} |
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{{libheader|Wren-fmt}} |
{{libheader|Wren-fmt}} |
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These are what are called 'multiplicatively perfect numbers' (see [https://oeis.org/A007422 OEIS-A00742]). |
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If this is intended to be a draft task, then I think the title should be changed to that. |
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<syntaxhighlight lang="ecmascript">import "./math" for Int, Nums |
<syntaxhighlight lang="ecmascript">import "./math" for Int, Nums |
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import "./fmt" for Fmt |
import "./fmt" for Fmt |
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var limit = 500 |
var limit = 500 |
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var count = 0 |
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System.print("Special numbers under %(limit):") |
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var i = 0 |
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for (i in 1...limit) { |
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System.print("Multiplicatively perfect numbers under %(limit):") |
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while (true) { |
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var pd = Int.properDivisors(i).skip(1) |
var pd = Int.properDivisors(i).skip(1) |
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if (pd.count > 1 && Nums.prod(pd) == i) { |
if (pd.count > 1 && Nums.prod(pd) == i) { |
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count = count + 1 |
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if (i < 500) { |
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var pds = pd.map { |d| Fmt.d(3, d) }.join(" x ") |
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Fmt.write("$3d = $s ", i, pds) |
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if (count % 4 == 0) System.print() |
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} |
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} |
} |
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if (i == 499) System.print("\n") |
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if (i >= limit - 1) { |
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var squares = Int.primeSieve((limit - 1).sqrt.floor).count |
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var cubes = Int.primeSieve((limit - 1).cbrt.floor).count |
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var count2 = count + squares - cubes |
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Fmt.print("Counts under $,7d: MPNs = $,7d Semi-primes = $,7d", limit, count, count2) |
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if (limit == 500000) return |
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limit = limit * 10 |
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} |
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i = i + 1 |
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}</syntaxhighlight> |
}</syntaxhighlight> |
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{{out}} |
{{out}} |
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<pre> |
<pre> |
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Multiplicatively perfect numbers under 500: |
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6 = 2 x 3 |
6 = 2 x 3 8 = 2 x 4 10 = 2 x 5 14 = 2 x 7 |
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15 = 3 x 5 21 = 3 x 7 22 = 2 x 11 26 = 2 x 13 |
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8 = 2 x 4 |
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27 = 3 x 9 33 = 3 x 11 34 = 2 x 17 35 = 5 x 7 |
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10 = 2 x 5 |
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38 = 2 x 19 39 = 3 x 13 46 = 2 x 23 51 = 3 x 17 |
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14 = 2 x 7 |
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55 = 5 x 11 57 = 3 x 19 58 = 2 x 29 62 = 2 x 31 |
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15 = 3 x 5 |
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65 = 5 x 13 69 = 3 x 23 74 = 2 x 37 77 = 7 x 11 |
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21 = 3 x 7 |
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82 = 2 x 41 85 = 5 x 17 86 = 2 x 43 87 = 3 x 29 |
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22 = 2 x 11 |
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91 = 7 x 13 93 = 3 x 31 94 = 2 x 47 95 = 5 x 19 |
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26 = 2 x 13 |
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106 = 2 x 53 111 = 3 x 37 115 = 5 x 23 118 = 2 x 59 |
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27 = 3 x 9 |
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119 = 7 x 17 122 = 2 x 61 123 = 3 x 41 125 = 5 x 25 |
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33 = 3 x 11 |
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129 = 3 x 43 133 = 7 x 19 134 = 2 x 67 141 = 3 x 47 |
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34 = 2 x 17 |
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142 = 2 x 71 143 = 11 x 13 145 = 5 x 29 146 = 2 x 73 |
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35 = 5 x 7 |
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155 = 5 x 31 158 = 2 x 79 159 = 3 x 53 161 = 7 x 23 |
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38 = 2 x 19 |
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166 = 2 x 83 177 = 3 x 59 178 = 2 x 89 183 = 3 x 61 |
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39 = 3 x 13 |
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185 = 5 x 37 187 = 11 x 17 194 = 2 x 97 201 = 3 x 67 |
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46 = 2 x 23 |
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202 = 2 x 101 203 = 7 x 29 205 = 5 x 41 206 = 2 x 103 |
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51 = 3 x 17 |
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209 = 11 x 19 213 = 3 x 71 214 = 2 x 107 215 = 5 x 43 |
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55 = 5 x 11 |
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217 = 7 x 31 218 = 2 x 109 219 = 3 x 73 221 = 13 x 17 |
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57 = 3 x 19 |
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226 = 2 x 113 235 = 5 x 47 237 = 3 x 79 247 = 13 x 19 |
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58 = 2 x 29 |
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249 = 3 x 83 253 = 11 x 23 254 = 2 x 127 259 = 7 x 37 |
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62 = 2 x 31 |
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262 = 2 x 131 265 = 5 x 53 267 = 3 x 89 274 = 2 x 137 |
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65 = 5 x 13 |
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278 = 2 x 139 287 = 7 x 41 291 = 3 x 97 295 = 5 x 59 |
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69 = 3 x 23 |
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298 = 2 x 149 299 = 13 x 23 301 = 7 x 43 302 = 2 x 151 |
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74 = 2 x 37 |
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303 = 3 x 101 305 = 5 x 61 309 = 3 x 103 314 = 2 x 157 |
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77 = 7 x 11 |
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319 = 11 x 29 321 = 3 x 107 323 = 17 x 19 326 = 2 x 163 |
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82 = 2 x 41 |
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327 = 3 x 109 329 = 7 x 47 334 = 2 x 167 335 = 5 x 67 |
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85 = 5 x 17 |
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339 = 3 x 113 341 = 11 x 31 343 = 7 x 49 346 = 2 x 173 |
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86 = 2 x 43 |
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355 = 5 x 71 358 = 2 x 179 362 = 2 x 181 365 = 5 x 73 |
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87 = 3 x 29 |
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371 = 7 x 53 377 = 13 x 29 381 = 3 x 127 382 = 2 x 191 |
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91 = 7 x 13 |
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386 = 2 x 193 391 = 17 x 23 393 = 3 x 131 394 = 2 x 197 |
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93 = 3 x 31 |
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395 = 5 x 79 398 = 2 x 199 403 = 13 x 31 407 = 11 x 37 |
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94 = 2 x 47 |
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411 = 3 x 137 413 = 7 x 59 415 = 5 x 83 417 = 3 x 139 |
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95 = 5 x 19 |
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422 = 2 x 211 427 = 7 x 61 437 = 19 x 23 445 = 5 x 89 |
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106 = 2 x 53 |
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446 = 2 x 223 447 = 3 x 149 451 = 11 x 41 453 = 3 x 151 |
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111 = 3 x 37 |
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454 = 2 x 227 458 = 2 x 229 466 = 2 x 233 469 = 7 x 67 |
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115 = 5 x 23 |
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471 = 3 x 157 473 = 11 x 43 478 = 2 x 239 481 = 13 x 37 |
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118 = 2 x 59 |
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482 = 2 x 241 485 = 5 x 97 489 = 3 x 163 493 = 17 x 29 |
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119 = 7 x 17 |
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497 = 7 x 71 |
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123 = 3 x 41 |
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Counts under 500: MPNs = 149 Semi-primes = 153 |
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125 = 5 x 25 |
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Counts under 5,000: MPNs = 1,353 Semi-primes = 1,365 |
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129 = 3 x 43 |
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Counts under 50,000: MPNs = 12,073 Semi-primes = 12,110 |
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133 = 7 x 19 |
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Counts under 500,000: MPNs = 108,222 Semi-primes = 108,326 |
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134 = 2 x 67 |
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141 = 3 x 47 |
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142 = 2 x 71 |
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143 = 11 x 13 |
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145 = 5 x 29 |
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146 = 2 x 73 |
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155 = 5 x 31 |
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158 = 2 x 79 |
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159 = 3 x 53 |
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161 = 7 x 23 |
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166 = 2 x 83 |
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177 = 3 x 59 |
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178 = 2 x 89 |
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183 = 3 x 61 |
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185 = 5 x 37 |
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187 = 11 x 17 |
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194 = 2 x 97 |
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201 = 3 x 67 |
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202 = 2 x 101 |
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203 = 7 x 29 |
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205 = 5 x 41 |
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206 = 2 x 103 |
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209 = 11 x 19 |
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213 = 3 x 71 |
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214 = 2 x 107 |
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215 = 5 x 43 |
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217 = 7 x 31 |
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218 = 2 x 109 |
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219 = 3 x 73 |
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221 = 13 x 17 |
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226 = 2 x 113 |
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235 = 5 x 47 |
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237 = 3 x 79 |
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247 = 13 x 19 |
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249 = 3 x 83 |
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253 = 11 x 23 |
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254 = 2 x 127 |
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259 = 7 x 37 |
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262 = 2 x 131 |
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265 = 5 x 53 |
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267 = 3 x 89 |
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274 = 2 x 137 |
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278 = 2 x 139 |
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287 = 7 x 41 |
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291 = 3 x 97 |
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295 = 5 x 59 |
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298 = 2 x 149 |
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299 = 13 x 23 |
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301 = 7 x 43 |
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302 = 2 x 151 |
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303 = 3 x 101 |
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305 = 5 x 61 |
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309 = 3 x 103 |
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314 = 2 x 157 |
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319 = 11 x 29 |
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321 = 3 x 107 |
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323 = 17 x 19 |
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326 = 2 x 163 |
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327 = 3 x 109 |
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329 = 7 x 47 |
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334 = 2 x 167 |
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335 = 5 x 67 |
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339 = 3 x 113 |
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341 = 11 x 31 |
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343 = 7 x 49 |
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346 = 2 x 173 |
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355 = 5 x 71 |
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358 = 2 x 179 |
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362 = 2 x 181 |
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365 = 5 x 73 |
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371 = 7 x 53 |
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377 = 13 x 29 |
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381 = 3 x 127 |
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382 = 2 x 191 |
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386 = 2 x 193 |
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391 = 17 x 23 |
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393 = 3 x 131 |
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394 = 2 x 197 |
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395 = 5 x 79 |
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398 = 2 x 199 |
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403 = 13 x 31 |
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407 = 11 x 37 |
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411 = 3 x 137 |
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413 = 7 x 59 |
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415 = 5 x 83 |
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417 = 3 x 139 |
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422 = 2 x 211 |
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427 = 7 x 61 |
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437 = 19 x 23 |
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445 = 5 x 89 |
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446 = 2 x 223 |
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447 = 3 x 149 |
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451 = 11 x 41 |
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453 = 3 x 151 |
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454 = 2 x 227 |
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458 = 2 x 229 |
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466 = 2 x 233 |
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469 = 7 x 67 |
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471 = 3 x 157 |
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473 = 11 x 43 |
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478 = 2 x 239 |
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481 = 13 x 37 |
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482 = 2 x 241 |
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485 = 5 x 97 |
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489 = 3 x 163 |
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493 = 17 x 29 |
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497 = 7 x 71 |
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</pre> |
</pre> |
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