Multiplicatively perfect numbers: Difference between revisions
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=Duplicate of task [[Semiprime]]= |
=Duplicate of task [[Semiprime]]= |
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Revision as of 22:42, 7 May 2023
Multiplicatively perfect numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
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
FreeBASIC
#define ceil(x) (-((-x*2.0-0.5) Shr 1))
Dim As Integer limit = 500
Dim As Integer n, pro, Divisors(), m, c = 0, ub
Print "Special numbers under"; limit; ":"
For n = 1 To limit
pro = 1
For m = 2 To ceil(n / 2)
If n Mod m = 0 Then
pro *= m
Redim Preserve Divisors(c) : Divisors(c) = m
c += 1
End If
Next m
ub = Ubound(Divisors)
If n = pro And ub > 1 Then
Print Using "### = ## x ###"; n; Divisors(ub-1); Divisors(ub)
End If
Next n
Sleep- Output:
Similar to Ring entry.
Phix
with javascript_semantics function special_numbers(integer n) return product(factors(n))=n end function sequence r = filter(tagset(500,2),special_numbers) printf(1,"%d special numbers under 500: %s\n", {length(r),join(shorten(r,"",5,"%d"),",")})
- Output:
149 special numbers under 500: 6,8,10,14,15,...,482,485,489,493,497
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
XPL0
func Special(N);
int N, D, P;
[D:= 2; P:= 1;
while D < N do
[if rem(N/D) = 0 then P:= P*D;
D:= D+1;
];
return P = N;
];
int N, C;
[C:= 0;
Format(4, 0);
for N:= 2 to 500-1 do
if Special(N) then
[RlOut(0, float(N));
C:= C+1;
if rem(C/20) = 0 then CrLf(0);
];
]- Output:
6 8 10 14 15 21 22 26 27 33 34 35 38 39 46 51 55 57 58 62 65 69 74 77 82 85 86 87 91 93 94 95 106 111 115 118 119 122 123 125 129 133 134 141 142 143 145 146 155 158 159 161 166 177 178 183 185 187 194 201 202 203 205 206 209 213 214 215 217 218 219 221 226 235 237 247 249 253 254 259 262 265 267 274 278 287 291 295 298 299 301 302 303 305 309 314 319 321 323 326 327 329 334 335 339 341 343 346 355 358 362 365 371 377 381 382 386 391 393 394 395 398 403 407 411 413 415 417 422 427 437 445 446 447 451 453 454 458 466 469 471 473 478 481 482 485 489 493 497