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If the product of the divisors of an integer n (including n itself) is equal to n^2, then n is a ''multiplicatively perfect number''.
EquivalentlyAlternatively: the product of the proper divisors of n (i.e. excluding n) is equal to n.
 
Note that the integer '1' qualifies under the first definition (1 = 1 x 1), but not under the second since '1' has no proper divisors. Given this ambiguity, it is optional whether '1' is included or not in solutions to this task.
<br>
;Task
Line 15 ⟶ 17:
* The OEIS sequence: &nbsp;[[oeis:A007422|A007422: Multiplicatively perfect numbers]]&nbsp;
<br><br>
 
=={{header|ALGOL 68}}==
{{libheader|ALGOL 68-primes}}
Uses sieves, counts 1 as a multiplicatively perfect number.<br>
As with the Phix and probably other samples, uses the fact that the multiplicatively perfect numbers (other than 1) must have three proper divisors - see OIES A007422.
<syntaxhighlight lang="algol68">
BEGIN # find multiplicatively perfect numbers - numbers whose proper #
# divisor product is the number itself ( includes 1 ) #
PR read "primes.incl.a68" PR # include prime utilties #
INT max number = 500 000; # largest number we wlil consider #
[]BOOL prime = PRIMESIEVE max number; # sieve the primes to max number #
[ 1 : max number ]INT pdc; # table of proper divisor counts #
[ 1 : max number ]INT pfc; # table of prime factor counts #
# count the proper divisors and prime factors #
FOR n TO UPB pdc DO pdc[ n ] := 1; pfc[ n ] := 0 OD;
FOR i FROM 2 TO UPB pdc DO
BOOL is prime = prime[ i ];
INT m := 1; # j will be the mth multiple of i #
FOR j FROM i + i BY i TO UPB pdc DO
pdc[ j ] +:= 1;
IF prime[ m +:= 1 ] THEN # j is a prime multiple of i #
pfc[ j ] +:= 1;
IF i = m THEN # j is i squared #
pfc[ j ] +:= 1
FI
ELSE # j is not a prime multiple of i #
pfc[ j ] +:= pfc[ m ] # add the prime factor count of m #
FI
OD
OD;
# find the mutiplicatively perfect numbers #
INT mp count := 0;
INT sp count := 0;
INT next to show := 500;
FOR n TO UPB pdc DO
IF n = 1 OR pdc[ n ] = 3 THEN
# n is 1 or has 3 proper divisors so is multiplicatively perfect #
# number - see OEIS A007422 #
mp count +:= 1;
IF n < 500 THEN
print( ( " ", whole( n, -3 ) ) );
IF mp count MOD 10 = 0 THEN print( ( newline ) ) FI
FI
FI;
IF pfc[ n ] = 2 THEN
# 2 prime factors, n is semi-prime #
sp count +:= 1
FI;
IF n = next to show THEN
print( ( "Up to ", whole( next to show, -8 )
, " there are ", whole( mp count, -6 )
, " multiplicatively perfect numbers and ", whole( sp count, -6 )
, " semi-primes", newline
)
);
next to show *:= 10
FI
OD
END
</syntaxhighlight>
{{out}}
<pre>
1 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
Up to 500 there are 150 multiplicatively perfect numbers and 153 semi-primes
Up to 5000 there are 1354 multiplicatively perfect numbers and 1365 semi-primes
Up to 50000 there are 12074 multiplicatively perfect numbers and 12110 semi-primes
Up to 500000 there are 108223 multiplicatively perfect numbers and 108326 semi-primes
</pre>
 
=={{header|BASIC}}==
==={{header|BASIC256}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vb">arraybase 1
limit = 500
dim Divisors(1)
c = 0
 
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
c += 1
redim Divisors(c)
Divisors[c] = m
end if
next m
ub = Divisors[?]
if n = pro and ub > 2 then
print rjust(string(n), 3); " = "; rjust(string(Divisors[ub-1]), 2); " x "; rjust(string(Divisors[ub]), 3)
end if
next n</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
 
==={{header|True BASIC}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="qbasic">LET limit = 50
DIM divisors(0)
LET c = 1
 
PRINT "Special numbers under"; limit; ":"
 
FOR n = 1 TO limit
LET pro = 1
FOR m = 2 TO ceil(n/2)
IF remainder(n, m) = 0 THEN
LET pro = pro*m
MAT REDIM divisors(c)
LET divisors(c) = m
LET c = c+1
END IF
NEXT m
LET ub = UBOUND(divisors)
IF n = pro AND ub > 1 THEN PRINT USING "### = ## x ###": n, divisors(ub-1), divisors(ub)
NEXT n
END</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
 
==={{header|PureBasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vb">Macro Ceil (_x_)
Round(_x_, #PB_Round_Up)
EndMacro
 
OpenConsole()
Define.i limit = 500
Dim Divisors.i(1)
Define.i n, pro, m, c = 0, ub
 
PrintN("Special numbers under" + Str(limit) + ":")
 
For n = 1 To limit
pro = 1
For m = 2 To Ceil(n / 2)
If Mod(n, m) = 0:
pro * m
ReDim Divisors(c) : Divisors(c) = m
c + 1
EndIf
Next m
ub = ArraySize(Divisors())
If n = pro And ub > 1:
PrintN(RSet(Str(n),3) + " = " + RSet(Str(Divisors(ub-1)),2) + " x " + RSet(Str(Divisors(ub)),3))
EndIf
Next n
Input()
CloseConsole()</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
 
==={{header|Yabasic}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vb">limit = 500
dim Divisors(1)
c = 1
 
print "Special numbers under", limit, ":"
 
for n = 1 to limit
pro = 1
for m = 2 to ceil(n / 2)
if mod(n, m) = 0 then
pro = pro * m
dim Divisors(c) : Divisors(c) = m
c = c + 1
fi
next m
ub = arraysize(Divisors(), 1)
if n = pro and ub > 1 then
print n using "###", " = ", Divisors(ub-1) using "##", " x ", Divisors(ub) using "###"
fi
next n</syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
 
=={{header|C}}==
This includes '1' as an MPN. Run time around 2.3 seconds.
<syntaxhighlight lang="c">#include <stdio.h>
#include <stdbool.h>
#include <locale.h>
 
bool isPrime(int n) {
if (n < 2) return false;
if (n%2 == 0) return n == 2;
if (n%3 == 0) return n == 3;
int d = 5;
while (d*d <= n) {
if (n%d == 0) return false;
d += 2;
if (n%d == 0) return false;
d += 4;
}
return true;
}
 
void divisors(int n, int *divs, int *length) {
int i, j, k = 1, c = 0;
if (n%2) k = 2;
for (i = 1; i*i <= n; i += k) {
if (i == 1) continue; // exclude 1 and n
if (!(n%i)) {
divs[c++] = i;
if (c > 2) break; // not eligible if has > 2 divisors
j = n / i;
if (j != i) divs[c++] = j;
}
}
*length = c;
}
 
int main() {
int i, d, j, k, t, length, prod;
int divs[4], count = 0, limit = 500, s = 3, c = 3, squares = 1, cubes = 1;
printf("Multiplicatively perfect numbers under %d:\n", limit);
setlocale(LC_NUMERIC, "");
for (i = 1; ; ++i) {
if (i != 1) {
divisors(i, divs, &length);
} else {
divs[1] = divs[0] = 1;
length = 2;
}
if (length == 2 && divs[0] * divs[1] == i) {
++count;
if (i < 500) {
printf("%3d ", i);
if (!(count%10)) printf("\n");
}
}
if (i == 499) printf("\n");
if (i >= limit - 1) {
for (j = s; j * j < limit; j += 2) if (isPrime(j)) ++squares;
for (k = c; k * k * k < limit; k +=2 ) if (isPrime(k)) ++cubes;
t = count + squares - cubes - 1;
printf("Counts under %'9d: MPNs = %'7d Semi-primes = %'7d\n", limit, count, t);
if (limit == 5000000) break;
s = j;
c = k;
limit *= 10;
}
}
return 0;
}</syntaxhighlight>
 
{{out}}
<pre>
Multiplicatively perfect numbers under 500:
1 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
 
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>
 
=={{header|C++}}==
<syntaxhighlight lang=C++>#include <iostream>
#include <vector>
#include <numeric>
 
std::vector<int> divisors( int n ) {
std::vector<int> divisors ;
for ( int i = 1 ; i < n + 1 ; i++ ) {
if ( n % i == 0 )
divisors.push_back( i ) ;
}
return divisors ;
}
 
int main( ) {
std::vector<int> multi_perfect ;
for ( int i = 1 ; i < 501 ; i++ ) {
std::vector<int> divis { divisors( i ) } ;
if ( std::accumulate( divis.begin( ) , divis.end( ) , 1 ,
std::multiplies<int>() ) == (i * i ) )
multi_perfect.push_back( i ) ;
}
std::cout << '(' ;
int count = 1 ;
for ( int i : multi_perfect ) {
std::cout << i << ' ' ;
if ( count % 15 == 0 )
std::cout << '\n' ;
count++ ;
}
std::cout << ")\n" ;
return 0 ;
}</syntaxhighlight>
{{out}}
<pre>
(1 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
)
</pre>
 
=={{header|FreeBASIC}}==
Line 40 ⟶ 377:
{{out}}
<pre>Similar to Ring entry.</pre>
 
=={{header|Go}}==
{{trans|C}}
{{libheader|Go-rcu}}
Run time around 9.2 seconds.
<syntaxhighlight lang="go">package main
 
import (
"fmt"
"rcu"
)
 
// library method customized for this task
func Divisors(n int) []int {
var divisors []int
i := 1
k := 1
if n%2 == 1 {
k = 2
}
for ; i*i <= n; i += k {
if i > 1 && n%i == 0 { // exclude 1 and n
divisors = append(divisors, i)
if len(divisors) > 2 { // not eligible if has > 2 divisors
break
}
j := n / i
if j != i {
divisors = append(divisors, j)
}
}
}
return divisors
}
 
func main() {
count := 0
limit := 500
s := 3
c := 3
squares := 1
cubes := 1
fmt.Printf("Multiplicatively perfect numbers under %d:\n", limit)
var divs []int
for i := 0; ; i++ {
if i != 1 {
divs = Divisors(i)
} else {
divs = []int{1, 1}
}
if len(divs) == 2 && divs[0]*divs[1] == i {
count++
if i < 500 {
fmt.Printf("%3d ", i)
if count%10 == 0 {
fmt.Println()
}
}
}
if i == 499 {
fmt.Println()
}
if i >= limit-1 {
var j, k int
for j = s; j*j < limit; j += 2 {
if rcu.IsPrime(j) {
squares++
}
}
for k = c; k*k*k < limit; k += 2 {
if rcu.IsPrime(k) {
cubes++
}
}
t := count + squares - cubes - 1
slimit := rcu.Commatize(limit)
scount := rcu.Commatize(count)
st := rcu.Commatize(t)
fmt.Printf("Counts under %9s: MPNs = %7s Semi-primes = %7s\n", slimit, scount, st)
if limit == 5000000 {
break
}
s, c = j, k
limit *= 10
}
}
}</syntaxhighlight>
 
{{out}}
<pre>
Same as C example.
</pre>
 
=={{header|Haskell}}==
<syntaxhighlight lang=Haskell>
divisors :: Int -> [Int]
divisors n = [d | d <- [1..n] , mod n d == 0 ]
 
isMultiplicativelyPerfect :: Int -> Bool
isMultiplicativelyPerfect n = (product $ divisors n) == n ^ 2
 
solution :: [Int]
solution = filter isMultiplicativelyPerfect [1..500]
</syntaxhighlight>
{{out}}
<pre>
[1,6,8,10,14,15,21,22,26,27,33,34,35,38,39,46,51,55,57,58,62,65,69,74,77,82,85,86,87,91,93,94,95,106,111,115,118,119,122,123,125,129,133,134,141,142,143,145,146,155,158,159,161,166,177,178,183,185,187,194,201,202,203,205,206,209,213,214,215,217,218,219,221,226,235,237,247,249,253,254,259,262,265,267,274,278,287,291,295,298,299,301,302,303,305,309,314,319,321,323,326,327,329,334,335,339,341,343,346,355,358,362,365,371,377,381,382,386,391,393,394,395,398,403,407,411,413,415,417,422,427,437,445,446,447,451,453,454,458,466,469,471,473,478,481,482,485,489,493,497]
</pre>
 
=={{header|J}}==
 
Implementation:
 
<syntaxhighlight lang=J>factors=: [: /:~@, */&>@{@((^ i.@>:)&.>/)@q:~&__
isMPerfect=: *: = */@(factors ::_:)"0</syntaxhighlight>
 
Task example:
 
<syntaxhighlight lang=J> #(#~ isMPerfect) i.500
150
10 15$(#~ isMPerfect) i.500
1 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</syntaxhighlight>
 
For the stretch goal, we need to determine the number of semi-primes, given the number of multiplicatively perfect numbers less than N:
 
<syntaxhighlight lang=J>adjSemiPrime=: + _1 + %: -&(p:inv) 3&%:</syntaxhighlight>
 
Thus (first number in following results is count of multiplicatively perfect numbers, second is count of semiprimes):
 
<syntaxhighlight lang=J> {{ (, adjSemiPrime&y) +/isMPerfect i.y}} 500
150 153
{{ (, adjSemiPrime&y) +/isMPerfect i.y}} 5000
1354 1365
{{ (, adjSemiPrime&y) +/isMPerfect i.y}} 50000
12074 12110
{{ (, adjSemiPrime&y) +/isMPerfect i.y}} 500000
108223 108326</syntaxhighlight>
 
=={{header|Julia}}==
<syntaxhighlight lang="julia">using Printf
using Primes
 
 
""" Find and count multiplicatively perfect integers up to thresholds """
function testmultiplicativelyperfects(thresholds = [500, 5000, 50_000, 500_000])
mpcount, scount = 0, 0
pmask = primesmask(thresholds[end])
println("Multiplicatively perfect numbers under $(thresholds[begin]):")
for n in 1:thresholds[end]
f = factor(n).pe
flen = length(f)
if flen == 2 && f[1][2] == 1 == f[2][2] || flen == 1 && f[1][2] == 3
mpcount += 1
if n < thresholds[begin]
@printf("%3d * %3d = %3d ", f[1][1], n ÷ f[1][1], n)
mpcount % 5 == 0 && println()
end
end
if n in thresholds
cbsum, sqsum = sum(pmask[1:Int(floor(n^(1/3)))]), sum(pmask[1:isqrt(n)])
scount = mpcount - cbsum + sqsum
@printf("\nCounts under %d: MPNs = %7d Semi-primes = %7d\n", n, mpcount, scount)
end
end
end
 
testmultiplicativelyperfects()
</syntaxhighlight>{{out}}
<pre>
 
Multiplicatively perfect numbers under 500:
2 * 3 = 6 2 * 4 = 8 2 * 5 = 10 2 * 7 = 14 3 * 5 = 15
3 * 7 = 21 2 * 11 = 22 2 * 13 = 26 3 * 9 = 27 3 * 11 = 33
2 * 17 = 34 5 * 7 = 35 2 * 19 = 38 3 * 13 = 39 2 * 23 = 46
3 * 17 = 51 5 * 11 = 55 3 * 19 = 57 2 * 29 = 58 2 * 31 = 62
5 * 13 = 65 3 * 23 = 69 2 * 37 = 74 7 * 11 = 77 2 * 41 = 82
5 * 17 = 85 2 * 43 = 86 3 * 29 = 87 7 * 13 = 91 3 * 31 = 93
2 * 47 = 94 5 * 19 = 95 2 * 53 = 106 3 * 37 = 111 5 * 23 = 115
2 * 59 = 118 7 * 17 = 119 2 * 61 = 122 3 * 41 = 123 5 * 25 = 125
3 * 43 = 129 7 * 19 = 133 2 * 67 = 134 3 * 47 = 141 2 * 71 = 142
11 * 13 = 143 5 * 29 = 145 2 * 73 = 146 5 * 31 = 155 2 * 79 = 158
3 * 53 = 159 7 * 23 = 161 2 * 83 = 166 3 * 59 = 177 2 * 89 = 178
3 * 61 = 183 5 * 37 = 185 11 * 17 = 187 2 * 97 = 194 3 * 67 = 201
2 * 101 = 202 7 * 29 = 203 5 * 41 = 205 2 * 103 = 206 11 * 19 = 209
3 * 71 = 213 2 * 107 = 214 5 * 43 = 215 7 * 31 = 217 2 * 109 = 218
3 * 73 = 219 13 * 17 = 221 2 * 113 = 226 5 * 47 = 235 3 * 79 = 237
13 * 19 = 247 3 * 83 = 249 11 * 23 = 253 2 * 127 = 254 7 * 37 = 259
2 * 131 = 262 5 * 53 = 265 3 * 89 = 267 2 * 137 = 274 2 * 139 = 278
7 * 41 = 287 3 * 97 = 291 5 * 59 = 295 2 * 149 = 298 13 * 23 = 299
7 * 43 = 301 2 * 151 = 302 3 * 101 = 303 5 * 61 = 305 3 * 103 = 309
2 * 157 = 314 11 * 29 = 319 3 * 107 = 321 17 * 19 = 323 2 * 163 = 326
3 * 109 = 327 7 * 47 = 329 2 * 167 = 334 5 * 67 = 335 3 * 113 = 339
11 * 31 = 341 7 * 49 = 343 2 * 173 = 346 5 * 71 = 355 2 * 179 = 358
2 * 181 = 362 5 * 73 = 365 7 * 53 = 371 13 * 29 = 377 3 * 127 = 381
2 * 191 = 382 2 * 193 = 386 17 * 23 = 391 3 * 131 = 393 2 * 197 = 394
5 * 79 = 395 2 * 199 = 398 13 * 31 = 403 11 * 37 = 407 3 * 137 = 411
7 * 59 = 413 5 * 83 = 415 3 * 139 = 417 2 * 211 = 422 7 * 61 = 427
19 * 23 = 437 5 * 89 = 445 2 * 223 = 446 3 * 149 = 447 11 * 41 = 451
3 * 151 = 453 2 * 227 = 454 2 * 229 = 458 2 * 233 = 466 7 * 67 = 469
3 * 157 = 471 11 * 43 = 473 2 * 239 = 478 13 * 37 = 481 2 * 241 = 482
5 * 97 = 485 3 * 163 = 489 17 * 29 = 493 7 * 71 = 497
Counts under 500: MPNs = 149 Semi-primes = 153
 
Counts under 5000: MPNs = 1353 Semi-primes = 1365
 
Counts under 50000: MPNs = 12073 Semi-primes = 12110
 
Counts under 500000: MPNs = 108222 Semi-primes = 108326
</pre>
 
=={{header|Nim}}==
In our solution, 1 is not considered to be a multiplicatively perfect number.
 
Using 32 bits integers rather than 64 bits integers improves considerably the performance. With a limit set to 5_000_000 and 64 bits integers, the program runs in around 10 seconds. This time drops to 3 seconds if 32 bits integers are used.
<syntaxhighlight lang="Nim">import std/strformat
 
func isMPN(n: int32): bool =
## Return true if "n" is a multiplicatively perfect number.
## We consider than 1 is not an MPN.
var first, second = 0i32 # First and second proper divisors.
let delta = 1 + (n and 1)
var d = delta + 1
while d * d <= n:
if n mod d == 0:
if second != 0: return false # More than two proper divisors.
first = d
let q = n div d
if q != d: second = q
inc d, delta
result = first * second == n
 
### Task ###
var count = 0
for n in 1i32..499i32:
if n.isMPN:
inc count
stdout.write &"{n:3}"
stdout.write if count mod 10 == 0: '\n' else: ' '
echo '\n'
 
### Stretch task ###
 
func isPrime(n: int32): bool =
## Return true if "n" is prime.
if n < 2: return false
if (n and 1) == 0: return n == 2
if n mod 3 == 0: return n == 3
var k = 5
var delta = 2
while k * k <= n:
if n mod k == 0: return false
inc k, delta
delta = 6 - delta
result = true
 
var mpnCount = 0
var limit = 500i32
var ns, nc = 3i32
var squares, cubes = 1i32
var n = 1i32
while true:
inc n
if n == limit:
while ns * ns < limit:
if ns.isPrime: inc squares
inc ns, 2
while nc * nc * nc < limit:
if nc.isPrime: inc cubes
inc nc, 2
echo &"Under {limit} there are {mpnCount} MPNs and {mpnCount - cubes + squares} semi-primes."
if limit == 500_000: break
limit *= 10
if n.isMPN: inc mpnCount
</syntaxhighlight>
 
{{out]]
<pre> 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
 
Under 500 there are 149 MPNs and 153 semi-primes.
Under 5000 there are 1353 MPNs and 1365 semi-primes.
Under 50000 there are 12073 MPNs and 12110 semi-primes.
Under 500000 there are 108222 MPNs and 108326 semi-primes.
</pre>
 
=={{header|Perl}}==
{{trans|Raku}}
{{libheader|ntheory}}
<syntaxhighlight lang="perl" line>
use v5.36;
use enum <false true>;
use ntheory <is_prime nth_prime is_semiprime gcd>;
 
sub comma { reverse ((reverse shift) =~ s/.{3}\K/,/gr) =~ s/^,//r }
sub table (@V) { my $t = 10 * (my $w = 5); ( sprintf( ('%'.$w.'d')x@V, @V) ) =~ s/.{1,$t}\K/\n/gr }
 
sub find_factor ($n, $constant = 1) { # NB: required that n > 1
my($x, $rho, $factor) = (2, 1, 1);
while ($factor == 1) {
$rho *= 2;
my $fixed = $x;
for (0..$rho) {
$x = ( $x * $x + $constant ) % $n;
$factor = gcd(($x-$fixed), $n);
last if 1 < $factor;
}
}
$factor = find_factor($n, $constant+1) if $n == $factor;
$factor
}
 
# Call with range 1..$limit
sub is_mpn($n) {
state $cube = 1; $cube = 1 if $n == 1; # set and reset
$n == 1 ? return true : is_prime($n) ? return false : ();
++$cube, return true if $n == nth_prime($cube)**3;
my $factor = find_factor($n);
my $div = int $n/$factor;
return true if is_prime $factor and is_prime $div and $div != $factor;
false
}
 
say "Multiplicatively perfect numbers less than 500:\n" . table grep is_mpn($_), 1..499;
 
say 'There are:';
for my $limit (5e2, 5e3, 5e4, 5e5, 5e6) {
my($m,$s) = (0,0);
is_mpn $_ and $m++ for 1..$limit-1;
is_semiprime $_ and $s++ for 1..$limit-1;
printf "%8s MPNs less than %8s, %8s semiprimes\n", comma($m), $limit, comma $s
}
</syntaxhighlight>
{{out}}
<pre>
Multiplicatively perfect numbers less than 500:
1 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
 
There are:
150 MPNs less than 500, 153 semiprimes
1,354 MPNs less than 5000, 1,365 semiprimes
12,074 MPNs less than 50000, 12,110 semiprimes
108,223 MPNs less than 500000, 108,326 semiprimes
978,983 MPNs less than 5000000, 979,274 semi primes
</pre>
 
=={{header|Phix}}==
Includes 1, to exclude just start with multiplicatively_perfect_numbers = 0 and r = {}.
<!--<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;">n1</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_numbers1</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;">5e6</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: #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: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">5e2</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: #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>
<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>
149150 specialmultiplicatively perfect numbers under 500: 1,6,8,10,14,15,...,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>
 
=={{header|PL/M}}==
{{works with|8080 PL/M Compiler}} ... under CP/M (or an emulator)
<syntaxhighlight lang="plm">
100H: /* FIND MUKTIPLICATIVELY PERFECT NUMBERS - NUMBERS WHOSE PROPER */
/* DIVISOR PRODUCT IS THE NUMBER ITSELF */
/* NOTE THIS IS EQUIVALENT TO FINDING NUMBERS WITH 3 PROPER DIVISORS */
/* SEE OEIS A007422 */
 
/* CP/M BDOS SYSTEM CALL */
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
/* I/O ROUTINES */
PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PR$NL: PROCEDURE; CALL PR$CHAR( 0DH ); CALL PR$CHAR( 0AH ); END;
PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
V = N;
W = LAST( N$STR );
N$STR( W ) = '$';
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL PR$STRING( .N$STR( W ) );
END PR$NUMBER;
 
/* FIND THE NUMBERS UP TO 500 */
 
DECLARE PDC ( 501 )ADDRESS; /* TABLE OF PROPER DIVISOR COUNTS */
DECLARE ( I, J, COUNT ) ADDRESS;
 
/* COUNT THE PROPER DIVISORS OF NUMBERS TO 500 */
DO I = 0 TO LAST( PDC ); PDC( I ) = 1; END;
DO I = 2 TO LAST( PDC );
DO J = I + I TO LAST( PDC ) BY I;
PDC( J ) = PDC( J ) + 1;
END;
END;
PDC( 1 ) = 3; /* PRETEND 1 HAS 3 PROPER DIVISORS SO IT IS INCLUDED */
 
/* SHOW YHE MULTIPLICATIVELY PERFECT NUMBERS */
COUNT = 0;
DO I = 1 TO LAST( PDC );
IF PDC( I ) = 3 THEN DO;
CALL PR$CHAR( ' ' );
IF I < 100 THEN DO;
IF I < 10 THEN CALL PR$CHAR( ' ' );
CALL PR$CHAR( ' ' );
END;
CALL PR$NUMBER( I );
IF ( COUNT := COUNT + 1 ) MOD 10 = 0 THEN CALL PR$NL;
END;
END;
 
EOF
</syntaxhighlight>
{{out}}
<pre>
1 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
</pre>
 
=={{header|Raku}}==
 
<syntaxhighlight lang="raku" line>use List::Divvy;
use Lingua::EN::Numbers;
 
constant @primes = (^∞).grep: &is-prime;
constant @cubes = @primes.map: *³;
 
state $cube = 0;
sub is-mpn(Int $n ) {
return False if $n.is-prime;
if $n == @cubes[$cube] {
++$cube;
return True
}
my $factor = find-factor($n);
return True if ($factor.is-prime && ( my $div = $n div $factor ).is-prime && ($div != $factor));
False;
}
 
sub find-factor ( Int $n, $constant = 1 ) {
my $x = 2;
my $rho = 1;
my $factor = 1;
while $factor == 1 {
$rho *= 2;
my $fixed = $x;
for ^$rho {
$x = ( $x * $x + $constant ) % $n;
$factor = ( $x - $fixed ) gcd $n;
last if 1 < $factor;
}
}
$factor = find-factor( $n, $constant + 1 ) if $n == $factor;
$factor;
}
 
constant @mpn = lazy 1, |(2..*).grep: &is-mpn;
 
say 'Multiplicatively perfect numbers less than 500:';
put @mpn.&upto(500).batch(10)».fmt("%3d").join: "\n";
 
put "\nThere are:";
for 5e2, 5e3, 5e4, 5e5, 5e6 {
printf "%8s MPNs less than %9s, %7s semiprimes.\n",
comma(my $count = +@mpn.&upto($_)), .Int.&comma,
comma $count + @primes.map(*²).&upto($_) - @cubes.&upto($_) - 1;
}</syntaxhighlight>
{{out}}
<pre>Multiplicatively perfect numbers less than 500:
1 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
 
There are:
150 MPNs less than 500, 153 semiprimes.
1,354 MPNs less than 5,000, 1,365 semiprimes.
12,074 MPNs less than 50,000, 12,110 semiprimes.
108,223 MPNs less than 500,000, 108,326 semiprimes.
978,983 MPNs less than 5,000,000, 979,274 semiprimes.</pre>
 
=={{header|Ring}}==
Line 238 ⟶ 1,127:
497 = 7 x 71
done...
</pre>
 
=={{header|RPL}}==
{{works with|HP|49}}
≪ { 1 }
2 ROT '''FOR''' j
'''IF''' j SQ j DIVIS ΠLIST == '''THEN''' j + '''END'''
'''NEXT'''
≫ '<span style="color:blue">TASK</span>' STO
≪ (1,0)
2 ROT '''FOR''' j
j DIVIS
'''IF CASE'''
DUP SIZE DUP 4 > OVER " < '''THEN''' NOT '''END'''
3 == '''THEN''' 1 '''END'''
DUP 2 GET OVER 3 GET GCD 1 == '''END'''
'''THEN''' SWAP (0,1) + SWAP '''END'''
'''IF''' ΠLIST j SQ == '''THEN''' 1 + '''END'''
'''NEXT'''
≫ '<span style="color:blue">STRETCH</span>' STO
 
500 <span style="color:blue">TASK</span>
500 <span style="color:blue">STRETCH</span>
{{out}}
<pre>
2: { 1 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 }
1: (150,153)
</pre>
 
=={{header|Rust}}==
<syntaxhighlight lang="rust">fn divisors( num : u128 ) -> Vec<u128> {
(1..= num).filter( | &d | num % d == 0 ).collect( )
}
 
fn main() {
println!("{:?}" , (1..= 500).filter( | &d | {
let divis : Vec<u128> = divisors( d ) ;
let prod : u128 = divis.iter( ).product( ) ;
prod == d.checked_pow( 2 ).unwrap( )
}).collect::<Vec<u128>>( ) ) ;
}</syntaxhighlight>
{{out}}
<pre>
[1, 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]
</pre>
 
 
=={{header|Sidef}}==
<syntaxhighlight lang="ruby">func multiplicatively_perfect_numbers(N) {
[1] + semiprimes(N).grep{|n| isqrt(n**tau(n)) == n.sqr } + N.icbrt.primes.map { .cube } -> sort
}
 
say ("Terms <= 500: ", multiplicatively_perfect_numbers(500).join(' '), "\n")
 
for n in (500, 5_000, 50_000, 500_000) {
var M = multiplicatively_perfect_numbers(n)
say "There are #{M.len} MPNs and #{semiprime_count(n)} semiprimes <= #{n.commify}."
}</syntaxhighlight>
{{out}}
<pre>
Terms <= 500: 1 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
 
There are 150 MPNs and 153 semiprimes <= 500.
There are 1354 MPNs and 1365 semiprimes <= 5,000.
There are 12074 MPNs and 12110 semiprimes <= 50,000.
There are 108223 MPNs and 108326 semiprimes <= 500,000.
</pre>
 
Line 243 ⟶ 1,199:
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
This includes '1' as an MPN. Not very quick at around 112 seconds but reasonable for Wren.
These are what are called 'multiplicatively perfect numbers' (see [https://oeis.org/A007422 OEIS-A00742]).
<syntaxhighlight lang="wren">import "./math" for Int, Nums
 
If this is intended to be a draft task, then I think the title should be changed to that.
<syntaxhighlight lang="ecmascript">import "./math" for Int, Nums
import "./fmt" for Fmt
 
// library method customized for this task
var divisors = Fn.new { |n|
var divisors = []
var i = 1
var k = (n%2 == 0) ? 1 : 2
while (i <= n.sqrt) {
if (i > 1 && n%i == 0) { // exclude 1 and n
divisors.add(i)
if (divisors.count > 2) break // not eligible if has > 2 divisors
var j = (n/i).floor
if (j != i) divisors.add(j)
}
i = i + k
}
return divisors
}
 
var limit = 500
var count = 0
System.print("Special numbers under %(limit):")
forvar (i in= 1...limit) {
System.print("Multiplicatively perfect numbers under %(limit):")
var pd = Int.properDivisors(i).skip(1)
while (true) {
if (pd.count > 1 && Nums.prod(pd) == i) {
var pd = (i var pds != pd.map1) {? |d| Fmtdivisors.dcall(3, di) }.join(": x[1, ")1]
if (pd.count == 2 Fmt.print("$3d&& pd[0] =* $s",pd[1] i,== pdsi) {
count = count + 1
if (i < 500) {
var pds = Fmt.swrite("$3d x $3d", pd[0], pd[1])
Fmt.write("$3d = $s ", i, pds)
if (count % 5 == 0) System.print()
}
}
if (i == 499) System.print()
if (i >= limit - 1) {
var squares = Int.primeCount((limit - 1).sqrt.floor)
var cubes = Int.primeCount((limit - 1).cbrt.floor)
var count2 = count + squares - cubes - 1
Fmt.print("Counts under $,9d: MPNs = $,7d Semi-primes = $,7d", limit, count, count2)
if (limit == 5000000) return
limit = limit * 10
}
i = i + 1
}</syntaxhighlight>
 
{{out}}
<pre>
SpecialMultiplicatively perfect numbers under 500:
1 = 1 x 1 6 = 2 x 3 8 = 2 x 4 10 = 2 x 5 14 = 2 x 7
6 = 2 x 3
15 = 3 x 5 21 = 3 x 7 22 = 2 x 11 26 = 2 x 13 27 = 3 x 9
8 = 2 x 4
33 = 3 x 11 34 = 2 x 17 35 = 5 x 7 38 = 2 x 19 39 = 3 x 13
10 = 2 x 5
46 = 2 x 23 51 = 3 x 17 55 = 5 x 11 57 = 3 x 19 58 = 2 x 29
14 = 2 x 7
62 = 2 x 31 65 = 5 x 13 69 = 3 x 23 74 = 2 x 37 77 = 7 x 11
15 = 3 x 5
82 = 2 x 41 85 = 5 x 17 86 = 2 x 43 87 = 3 x 29 91 = 7 x 13
21 = 3 x 7
93 = 3 x 31 94 = 2 x 47 95 = 5 x 19 106 = 2 x 53 111 = 3 x 37
22 = 2 x 11
115 = 5 x 23 118 = 2 x 59 119 = 7 x 17 122 = 2 x 61 123 = 3 x 41
26 = 2 x 13
125 = 5 x 25 129 = 3 x 43 133 = 7 x 19 134 = 2 x 67 141 = 3 x 47
27 = 3 x 9
142 = 2 x 71 143 = 11 x 13 145 = 5 x 29 146 = 2 x 73 155 = 5 x 31
33 = 3 x 11
158 = 2 x 79 159 = 3 x 53 161 = 7 x 23 166 = 2 x 83 177 = 3 x 59
34 = 2 x 17
178 = 2 x 89 183 = 3 x 61 185 = 5 x 37 187 = 11 x 17 194 = 2 x 97
35 = 5 x 7
201 = 3 x 67 202 = 2 x 101 203 = 7 x 29 205 = 5 x 41 206 = 2 x 103
38 = 2 x 19
209 = 11 x 19 213 = 3 x 71 214 = 2 x 107 215 = 5 x 43 217 = 7 x 31
39 = 3 x 13
218 = 2 x 109 219 = 3 x 73 221 = 13 x 17 226 = 2 x 113 235 = 5 x 47
46 = 2 x 23
237 = 3 x 79 247 = 13 x 19 249 = 3 x 83 253 = 11 x 23 254 = 2 x 127
51 = 3 x 17
259 = 7 x 37 262 = 2 x 131 265 = 5 x 53 267 = 3 x 89 274 = 2 x 137
55 = 5 x 11
278 = 2 x 139 287 = 7 x 41 291 = 3 x 97 295 = 5 x 59 298 = 2 x 149
57 = 3 x 19
299 = 13 x 23 301 = 7 x 43 302 = 2 x 151 303 = 3 x 101 305 = 5 x 61
58 = 2 x 29
309 = 3 x 103 314 = 2 x 157 319 = 11 x 29 321 = 3 x 107 323 = 17 x 19
62 = 2 x 31
326 = 2 x 163 327 = 3 x 109 329 = 7 x 47 334 = 2 x 167 335 = 5 x 67
65 = 5 x 13
339 = 3 x 113 341 = 11 x 31 343 = 7 x 49 346 = 2 x 173 355 = 5 x 71
69 = 3 x 23
358 = 2 x 179 362 = 2 x 181 365 = 5 x 73 371 = 7 x 53 377 = 13 x 29
74 = 2 x 37
381 = 3 x 127 382 = 2 x 191 386 = 2 x 193 391 = 17 x 23 393 = 3 x 131
77 = 7 x 11
394 = 2 x 197 395 = 5 x 79 398 = 2 x 199 403 = 13 x 31 407 = 11 x 37
82 = 2 x 41
411 = 3 x 137 413 = 7 x 59 415 = 5 x 83 417 = 3 x 139 422 = 2 x 211
85 = 5 x 17
427 = 7 x 61 437 = 19 x 23 445 = 5 x 89 446 = 2 x 223 447 = 3 x 149
86 = 2 x 43
451 = 11 x 41 453 = 3 x 151 454 = 2 x 227 458 = 2 x 229 466 = 2 x 233
87 = 3 x 29
469 = 7 x 67 471 = 3 x 157 473 = 11 x 43 478 = 2 x 239 481 = 13 x 37
91 = 7 x 13
482 = 2 x 241 485 = 5 x 97 489 = 3 x 163 493 = 17 x 29 497 = 7 x 71
93 = 3 x 31
 
94 = 2 x 47
Counts under 500: MPNs = 150 Semi-primes = 153
95 = 5 x 19
Counts under 5,000: MPNs = 1,354 Semi-primes = 1,365
106 = 2 x 53
Counts under 50,000: MPNs = 12,074 Semi-primes = 12,110
111 = 3 x 37
Counts under 500,000: MPNs = 108,223 Semi-primes = 108,326
115 = 5 x 23
Counts under 5,000,000: MPNs = 978,983 Semi-primes = 979,274
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
</pre>
 
Ulrie
258

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Retrieved from "https://rosettacode.org/wiki/Special:MobileDiff/341791...363174"