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Revision as of 10:17, 20 April 2023
Duplicate of task Semiprime
Definition
If the product of the divisors of an integer n (other than 1 and n itself) is equal to the number itself, then n is a special number.
Task
Find and show on this page the Special numbers where n < 500
Ring
see "working..." + nl
see "Special numbers under 500:" + nl
limit = 500
Divisors = []
for n = 1 to limit
pro = 1
Divisors = []
for m = 2 to ceil(n/2)
if n % m = 0
pro = pro * m
add(Divisors,m)
ok
next
str = ""
if n = pro and len(Divisors) > 1
for m = 1 to len(Divisors)
str = str + Divisors[m] + " * "
if m = len(Divisors)
str = left(str,len(str)-2)
ok
next
see "" + n + " = " + str + nl
ok
next
see "done..." + nl- Output:
working...Special numbers under 500: 6 = 2 x 3 8 = 2 x 4 10 = 2 x 5 14 = 2 x 7 15 = 3 x 5 21 = 3 x 7 22 = 2 x 11 26 = 2 x 13 27 = 3 x 9 33 = 3 x 11 34 = 2 x 17 35 = 5 x 7 38 = 2 x 19 39 = 3 x 13 46 = 2 x 23 51 = 3 x 17 55 = 5 x 11 57 = 3 x 19 58 = 2 x 29 62 = 2 x 31 65 = 5 x 13 69 = 3 x 23 74 = 2 x 37 77 = 7 x 11 82 = 2 x 41 85 = 5 x 17 86 = 2 x 43 87 = 3 x 29 91 = 7 x 13 93 = 3 x 31 94 = 2 x 47 95 = 5 x 19 106 = 2 x 53 111 = 3 x 37 115 = 5 x 23 118 = 2 x 59 119 = 7 x 17 122 = 2 x 61 123 = 3 x 41 125 = 5 x 25 129 = 3 x 43 133 = 7 x 19 134 = 2 x 67 141 = 3 x 47 142 = 2 x 71 143 = 11 x 13 145 = 5 x 29 146 = 2 x 73 155 = 5 x 31 158 = 2 x 79 159 = 3 x 53 161 = 7 x 23 166 = 2 x 83 177 = 3 x 59 178 = 2 x 89 183 = 3 x 61 185 = 5 x 37 187 = 11 x 17 194 = 2 x 97 201 = 3 x 67 202 = 2 x 101 203 = 7 x 29 205 = 5 x 41 206 = 2 x 103 209 = 11 x 19 213 = 3 x 71 214 = 2 x 107 215 = 5 x 43 217 = 7 x 31 218 = 2 x 109 219 = 3 x 73 221 = 13 x 17 226 = 2 x 113 235 = 5 x 47 237 = 3 x 79 247 = 13 x 19 249 = 3 x 83 253 = 11 x 23 254 = 2 x 127 259 = 7 x 37 262 = 2 x 131 265 = 5 x 53 267 = 3 x 89 274 = 2 x 137 278 = 2 x 139 287 = 7 x 41 291 = 3 x 97 295 = 5 x 59 298 = 2 x 149 299 = 13 x 23 301 = 7 x 43 302 = 2 x 151 303 = 3 x 101 305 = 5 x 61 309 = 3 x 103 314 = 2 x 157 319 = 11 x 29 321 = 3 x 107 323 = 17 x 19 326 = 2 x 163 327 = 3 x 109 329 = 7 x 47 334 = 2 x 167 335 = 5 x 67 339 = 3 x 113 341 = 11 x 31 343 = 7 x 49 346 = 2 x 173 355 = 5 x 71 358 = 2 x 179 362 = 2 x 181 365 = 5 x 73 371 = 7 x 53 377 = 13 x 29 381 = 3 x 127 382 = 2 x 191 386 = 2 x 193 391 = 17 x 23 393 = 3 x 131 394 = 2 x 197 395 = 5 x 79 398 = 2 x 199 403 = 13 x 31 407 = 11 x 37 411 = 3 x 137 413 = 7 x 59 415 = 5 x 83 417 = 3 x 139 422 = 2 x 211 427 = 7 x 61 437 = 19 x 23 445 = 5 x 89 446 = 2 x 223 447 = 3 x 149 451 = 11 x 41 453 = 3 x 151 454 = 2 x 227 458 = 2 x 229 466 = 2 x 233 469 = 7 x 67 471 = 3 x 157 473 = 11 x 43 478 = 2 x 239 481 = 13 x 37 482 = 2 x 241 485 = 5 x 97 489 = 3 x 163 493 = 17 x 29 497 = 7 x 71 done...
Wren
These are what are called 'multiplicatively perfect numbers' (see OEIS-A00742).
If this is intended to be a draft task, then I think the title should be changed to that.
import "./math" for Int, Nums
import "./fmt" for Fmt
var limit = 500
System.print("Special numbers under %(limit):")
for (i in 1...limit) {
var pd = Int.properDivisors(i).skip(1)
if (pd.count > 1 && Nums.prod(pd) == i) {
var pds = pd.map { |d| Fmt.d(3, d) }.join(" x ")
Fmt.print("$3d = $s", i, pds)
}
}- Output:
Special numbers under 500: 6 = 2 x 3 8 = 2 x 4 10 = 2 x 5 14 = 2 x 7 15 = 3 x 5 21 = 3 x 7 22 = 2 x 11 26 = 2 x 13 27 = 3 x 9 33 = 3 x 11 34 = 2 x 17 35 = 5 x 7 38 = 2 x 19 39 = 3 x 13 46 = 2 x 23 51 = 3 x 17 55 = 5 x 11 57 = 3 x 19 58 = 2 x 29 62 = 2 x 31 65 = 5 x 13 69 = 3 x 23 74 = 2 x 37 77 = 7 x 11 82 = 2 x 41 85 = 5 x 17 86 = 2 x 43 87 = 3 x 29 91 = 7 x 13 93 = 3 x 31 94 = 2 x 47 95 = 5 x 19 106 = 2 x 53 111 = 3 x 37 115 = 5 x 23 118 = 2 x 59 119 = 7 x 17 122 = 2 x 61 123 = 3 x 41 125 = 5 x 25 129 = 3 x 43 133 = 7 x 19 134 = 2 x 67 141 = 3 x 47 142 = 2 x 71 143 = 11 x 13 145 = 5 x 29 146 = 2 x 73 155 = 5 x 31 158 = 2 x 79 159 = 3 x 53 161 = 7 x 23 166 = 2 x 83 177 = 3 x 59 178 = 2 x 89 183 = 3 x 61 185 = 5 x 37 187 = 11 x 17 194 = 2 x 97 201 = 3 x 67 202 = 2 x 101 203 = 7 x 29 205 = 5 x 41 206 = 2 x 103 209 = 11 x 19 213 = 3 x 71 214 = 2 x 107 215 = 5 x 43 217 = 7 x 31 218 = 2 x 109 219 = 3 x 73 221 = 13 x 17 226 = 2 x 113 235 = 5 x 47 237 = 3 x 79 247 = 13 x 19 249 = 3 x 83 253 = 11 x 23 254 = 2 x 127 259 = 7 x 37 262 = 2 x 131 265 = 5 x 53 267 = 3 x 89 274 = 2 x 137 278 = 2 x 139 287 = 7 x 41 291 = 3 x 97 295 = 5 x 59 298 = 2 x 149 299 = 13 x 23 301 = 7 x 43 302 = 2 x 151 303 = 3 x 101 305 = 5 x 61 309 = 3 x 103 314 = 2 x 157 319 = 11 x 29 321 = 3 x 107 323 = 17 x 19 326 = 2 x 163 327 = 3 x 109 329 = 7 x 47 334 = 2 x 167 335 = 5 x 67 339 = 3 x 113 341 = 11 x 31 343 = 7 x 49 346 = 2 x 173 355 = 5 x 71 358 = 2 x 179 362 = 2 x 181 365 = 5 x 73 371 = 7 x 53 377 = 13 x 29 381 = 3 x 127 382 = 2 x 191 386 = 2 x 193 391 = 17 x 23 393 = 3 x 131 394 = 2 x 197 395 = 5 x 79 398 = 2 x 199 403 = 13 x 31 407 = 11 x 37 411 = 3 x 137 413 = 7 x 59 415 = 5 x 83 417 = 3 x 139 422 = 2 x 211 427 = 7 x 61 437 = 19 x 23 445 = 5 x 89 446 = 2 x 223 447 = 3 x 149 451 = 11 x 41 453 = 3 x 151 454 = 2 x 227 458 = 2 x 229 466 = 2 x 233 469 = 7 x 67 471 = 3 x 157 473 = 11 x 43 478 = 2 x 239 481 = 13 x 37 482 = 2 x 241 485 = 5 x 97 489 = 3 x 163 493 = 17 x 29 497 = 7 x 71