Data commit

Task/Arithmetic-derivative/00-META.yaml

@@ -0,0 +1,2 @@
+---
+from: http://rosettacode.org/wiki/Arithmetic_derivative

Task/Arithmetic-derivative/00-TASK.txt

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+The '''arithmetic derivative''' of an integer (more specifically, the
+'''Lagarias arithmetic derivative''') is a function defined for integers, based on prime
+factorization, by analogy with the product rule for the derivative of a function that is
+used in mathematical analysis. Accordingly, for natural numbers n, the arithmetic 
+derivative D(n) is defined as follows:
+
+;*D(0) = D(1) = 0.
+;*D(p) = 1 for any prime p.
+;*D(mn) = D(m)n + mD(n) for any m,n ∈ N. (Leibniz rule for derivatives).
+
+Additionally, for negative integers the arithmetic derivative may be defined as -D(-n) (n < 0).
+
+; Examples
+
+D(2) = 1 and D(3) = 1 (both are prime) so if mn = 2 * 3, D(6) = (1)(3) + (1)(2) = 5.
+
+D(9) = D(3)(3) + D(3)(3) = 6
+
+D(27) = D(3)*9 + D(9)*3 = 9 + 18 = 27
+
+D(30) = D(5)(6) + D(6)(5) = 6 + 5 * 5 = 31.
+
+; Task
+
+Find and show the arithmetic derivatives for -99 through 100.
+
+; Stretch task
+
+Find (the arithmetic derivative of 10^m) then divided by 7, where m is from 1 to 20.
+
+; See also
+
+;* [[oeis:A003415|OEIS:A003415 - a(n) = n' = arithmetic derivative of n.]]
+;*[[wp:Arithmetic_derivative|Wikipedia: Arithmetic Derivative]]
+
+

Task/Arithmetic-derivative/C++/arithmetic-derivative.cpp

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+#include <iomanip>
+#include <iostream>
+
+#include <boost/multiprecision/cpp_int.hpp>
+
+template <typename IntegerType>
+IntegerType arithmetic_derivative(IntegerType n) {
+    bool negative = n < 0;
+    if (negative)
+        n = -n;
+    if (n < 2)
+        return 0;
+    IntegerType sum = 0, count = 0, m = n;
+    while ((m & 1) == 0) {
+        m >>= 1;
+        count += n;
+    }
+    if (count > 0)
+        sum += count / 2;
+    for (IntegerType p = 3, sq = 9; sq <= m; p += 2) {
+        count = 0;
+        while (m % p == 0) {
+            m /= p;
+            count += n;
+        }
+        if (count > 0)
+            sum += count / p;
+        sq += (p + 1) << 2;
+    }
+    if (m > 1)
+        sum += n / m;
+    if (negative)
+        sum = -sum;
+    return sum;
+}
+
+int main() {
+    using boost::multiprecision::int128_t;
+
+    for (int n = -99, i = 0; n <= 100; ++n, ++i) {
+        std::cout << std::setw(4) << arithmetic_derivative(n)
+                  << ((i + 1) % 10 == 0 ? '\n' : ' ');
+    }
+
+    int128_t p = 10;
+    std::cout << '\n';
+    for (int i = 0; i < 20; ++i, p *= 10) {
+        std::cout << "D(10^" << std::setw(2) << i + 1
+                  << ") / 7 = " << arithmetic_derivative(p) / 7 << '\n';
+    }
+}

Task/Arithmetic-derivative/C/arithmetic-derivative.c

@@ -0,0 +1,76 @@
+#include <stdio.h>
+#include <stdint.h>
+
+typedef uint64_t u64;
+
+void primeFactors(u64 n, u64 *factors, int *length) {
+    if (n < 2) return;
+    int count = 0;
+    int inc[8] = {4, 2, 4, 2, 4, 6, 2, 6};
+    while (!(n%2)) {
+        factors[count++] = 2;
+        n /= 2;
+    }
+    while (!(n%3)) {
+        factors[count++] = 3;
+        n /= 3;
+    }
+    while (!(n%5)) {
+        factors[count++] = 5;
+        n /= 5;
+    }
+    for (u64 k = 7, i = 0; k*k <= n; ) {
+        if (!(n%k)) {
+            factors[count++] = k;
+            n /= k;
+        } else {
+            k += inc[i];
+            i = (i + 1) % 8;
+        }
+    }
+    if (n > 1) {
+        factors[count++] = n;
+    }
+    *length = count;
+}
+
+double D(double n) {
+    if (n < 0) return -D(-n);
+    if (n < 2) return 0;
+    int i, length;
+    double d;
+    u64 f[80], g;
+    if (n < 1e19) {
+        primeFactors((u64)n, f, &length);
+    } else {
+        g = (u64)(n / 100);
+        primeFactors(g, f, &length);
+        f[length+1] = f[length] = 2;
+        f[length+3] = f[length+2] = 5;
+        length += 4;
+    }
+    if (length == 1) return 1;
+    if (length == 2) return (double)(f[0] + f[1]);
+    d = n / (double)f[0];
+    return D(d) * (double)f[0] + d;
+}
+
+int main() {
+    u64 ad[200];
+    int n, m;
+    double pow;
+    for (n = -99; n < 101; ++n) {
+        ad[n+99] = (int)D((double)n);
+    }
+    for (n = 0; n < 200; ++n) {
+        printf("%4ld ", ad[n]);
+        if (!((n+1)%10)) printf("\n");
+    }
+    printf("\n");
+    pow = 1;
+    for (m = 1; m < 21; ++m) {
+        pow *= 10;
+        printf("D(10^%-2d) / 7 = %.0f\n", m, D(pow)/7);
+    }
+    return 0;
+}

Task/Arithmetic-derivative/Factor/arithmetic-derivative.factor

@@ -0,0 +1,13 @@
+USING: combinators formatting grouping io kernel math
+math.primes.factors prettyprint ranges sequences ;
+
+: n' ( m -- n )
+    {
+        { [ dup neg? ] [ neg n' neg ] }
+        { [ dup 2 < ] [ drop 0 ] }
+        { [ factors dup length 1 = ] [ drop 1 ] }
+        [ unclip-slice swap product 2dup n' * spin n' * + ]
+    } cond ;
+
+-99 100 [a..b] [ n' ] map 10 group
+[ [ "%5d" printf ] each nl ] each

Task/Arithmetic-derivative/Go/arithmetic-derivative.go

@@ -0,0 +1,46 @@
+package main
+
+import (
+    "fmt"
+    "rcu"
+)
+
+func D(n float64) float64 {
+    if n < 0 {
+        return -D(-n)
+    }
+    if n < 2 {
+        return 0
+    }
+    var f []int
+    if n < 1e19 {
+        f = rcu.PrimeFactors(int(n))
+    } else {
+        g := int(n / 100)
+        f = rcu.PrimeFactors(g)
+        f = append(f, []int{2, 2, 5, 5}...)
+    }
+    c := len(f)
+    if c == 1 {
+        return 1
+    }
+    if c == 2 {
+        return float64(f[0] + f[1])
+    }
+    d := n / float64(f[0])
+    return D(d)*float64(f[0]) + d
+}
+
+func main() {
+    ad := make([]int, 200)
+    for n := -99; n < 101; n++ {
+        ad[n+99] = int(D(float64(n)))
+    }
+    rcu.PrintTable(ad, 10, 4, false)
+    fmt.Println()
+    pow := 1.0
+    for m := 1; m < 21; m++ {
+        pow *= 10
+        fmt.Printf("D(10^%-2d) / 7 = %.0f\n", m, D(pow)/7)
+    }
+}

Task/Arithmetic-derivative/Haskell/arithmetic-derivative.hs

@@ -0,0 +1,32 @@
+import Control.Monad (forM_)
+import Data.List (intercalate)
+import Data.List.Split (chunksOf)
+import Math.NumberTheory.Primes (factorise, unPrime)
+import Text.Printf (printf)
+
+-- The arithmetic derivative of a number, which is assumed to be non-negative.
+arithderiv_ :: Integer -> Integer
+arithderiv_ 0 = 0
+arithderiv_ n = foldr step 0 $ factorise n
+  where step (p, v) s = s + n `quot` unPrime p * fromIntegral v
+
+-- The arithmetic derivative of any integer.
+arithderiv :: Integer -> Integer
+arithderiv n | n < 0     = negate $ arithderiv_ (negate n)
+             | otherwise = arithderiv_ n
+
+printTable :: [Integer] -> IO ()
+printTable = putStrLn
+           . intercalate "\n"
+           . map unwords
+           . chunksOf 10
+           . map (printf "%5d")
+
+main :: IO ()
+main = do
+  printTable [arithderiv n | n <- [-99..100]]
+  putStrLn ""
+  forM_ [1..20 :: Integer] $ \i ->
+    let q = 7
+        n = arithderiv (10^i) `quot` q
+    in printf "D(10^%-2d) / %d = %d\n" i q n

Task/Arithmetic-derivative/J/arithmetic-derivative-1.j

@@ -0,0 +1 @@
+D=: {{ +/y%q:1>.|y }}"0

Task/Arithmetic-derivative/J/arithmetic-derivative-2.j

@@ -0,0 +1,21 @@
+   D _99+i.20 10
+_75  _77  _1 _272 _24  _49 _34  _96  _20 _123
+ _1 _140 _32  _45 _22 _124  _1  _43 _108 _176
+ _1  _71 _18  _80 _55  _39  _1 _156   _1  _59
+_26  _72  _1  _61 _18 _192 _51  _33   _1  _92
+ _1  _31 _22  _92 _16  _81  _1  _56  _20  _45
+_14 _112  _1  _25 _39  _48  _1  _41   _1  _68
+_16  _21  _1  _60 _12  _19 _14  _80   _1  _31
+ _1  _32 _27  _15 _10  _44  _1  _13  _10  _24
+ _1  _21  _1  _32  _8   _9  _1  _16   _1   _7
+ _6  _12  _1   _5  _1   _4  _1   _1    0    0
+  0    1   1    4   1    5   1   12    6    7
+  1   16   1    9   8   32   1   21    1   24
+ 10   13   1   44  10   15  27   32    1   31
+  1   80  14   19  12   60   1   21   16   68
+  1   41   1   48  39   25   1  112   14   45
+ 20   56   1   81  16   92  22   31    1   92
+  1   33  51  192  18   61   1   72   26   59
+  1  156   1   39  55   80  18   71    1  176
+108   43   1  124  22   45  32  140    1  123
+ 20   96  34   49  24  272   1   77   75  140

Task/Arithmetic-derivative/J/arithmetic-derivative-3.j

@@ -0,0 +1,2 @@
+   15 10 6 + 2 3 5 * D 15 10 6
+31 31 31

Task/Arithmetic-derivative/J/arithmetic-derivative-4.j

@@ -0,0 +1,5 @@
+   (D 10x^1+i.4 5)%7
+                1                 20                 300                 4000                 50000
+           600000            7000000            80000000            900000000           10000000000
+     110000000000      1200000000000      13000000000000      140000000000000      1500000000000000
+16000000000000000 170000000000000000 1800000000000000000 19000000000000000000 200000000000000000000

Task/Arithmetic-derivative/Java/arithmetic-derivative.java

@@ -0,0 +1,38 @@
+import java.math.BigInteger;
+
+public final class ArithmeticDerivative {
+
+	public static void main(String[] aArgs) {
+        System.out.println("Arithmetic derivatives for -99 to 100 inclusive:");
+		for ( int n = -99, column = 0; n <= 100; n++ ) {
+			System.out.print(String.format("%4d%s",
+				derivative(BigInteger.valueOf(n)), ( ++column % 10 == 0 ) ? "\n" : " "));
+		}
+		System.out.println();
+		
+		final BigInteger seven = BigInteger.valueOf(7);
+		for ( int power = 1; power <= 20; power++ ) {
+			System.out.println(String.format("%s%2d%s%d",
+				"D(10^", power, ") / 7 = ", derivative(BigInteger.TEN.pow(power)).divide(seven)));
+		}
+	}
+	
+	private static BigInteger derivative(BigInteger aNumber) {
+		if ( aNumber.signum() == -1 ) {
+			return derivative(aNumber.negate()).negate();
+		}
+		if ( aNumber == BigInteger.ZERO || aNumber == BigInteger.ONE ) {
+			return BigInteger.ZERO;
+		}
+		BigInteger divisor = BigInteger.TWO;
+		while ( divisor.multiply(divisor).compareTo(aNumber) <= 0 ) {
+		    if ( aNumber.mod(divisor).signum() == 0 ) {
+		        final BigInteger quotient = aNumber.divide(divisor);
+		        return quotient.multiply(derivative(divisor)).add(divisor.multiply(derivative(quotient)));
+		    }
+		    divisor = divisor.add(BigInteger.ONE);
+		}
+		return BigInteger.ONE;
+	}
+
+}

Task/Arithmetic-derivative/Jq/arithmetic-derivative.jq

@@ -0,0 +1,34 @@
+To take advantage of gojq's arbitrary-precision integer arithmetic:
+def power($b): . as $in | reduce range(0;$b) as $i (1; . * $in);
+
+# In case gojq is used:
+def _nwise($n):
+  def nw: if length <= $n then . else .[0:$n] , (.[$n:] | nw) end;
+  nw;
+
+def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
+
+def D($n):
+    if   $n < 0 then -D(- $n)
+    elif $n < 2 then 0
+    else [$n | factors] as $f
+    | ($f|length) as $c
+    | if   $c <= 1 then 1
+      elif $c == 2 then $f[0] + $f[1]
+      else ($n / $f[0]) as $d
+      | D($d) * $f[0] + $d
+      end
+    end ;
+
+def task:
+  def task1:
+    reduce range(-99; 101) as $n ([]; .[$n+99] = D($n))
+    | _nwise(10) | map(lpad(4)) | join(" ");
+
+  def task2:
+    range(1; 21) as $i
+    | "D(10^\($i)) / 7 = \( D(10|power($i))/7 )" ;
+
+  task1, "", task2 ;
+
+task

Task/Arithmetic-derivative/Julia/arithmetic-derivative.julia

@@ -0,0 +1,10 @@
+using Primes
+
+D(n) = n < 0 ? -D(-n) : n < 2 ? zero(n) : isprime(n) ? one(n) : typeof(n)(sum(e * n ÷ p for (p, e) in eachfactor(n)))
+
+foreach(p -> print(lpad(p[2], 5), p[1] % 10 == 0 ? "\n" : ""), pairs(map(D, -99:100)))
+
+println()
+for m in 1:20
+    println("D for 10^", rpad(m, 3), "divided by 7 is ", D(Int128(10)^m) ÷ 7)
+end

Task/Arithmetic-derivative/Nim/arithmetic-derivative.nim

@@ -0,0 +1,46 @@
+import std/[strformat, strutils]
+import integers
+
+
+func aDerivative(n: int | Integer): typeof(n) =
+  ## Recursively compute the arithmetic derivative.
+  ## The function works with normal integers or big integers.
+  ## Using a cache to store the derivatives would improve the
+  ## performance, but this is not needed for these tasks.
+  if n < 0: return -aDerivative(-n)
+  if n == 0 or n == 1: return 0
+  if n == 2: return 1
+  var d = 2
+  result = 1
+  while d * d <= n:
+    if n mod d == 0:
+      let q = n div d
+      result = q * aDerivative(d) + d * aDerivative(q)
+      break
+    inc d
+
+
+### Task ###
+
+echo "Arithmetic derivatives for -99 through 100:"
+
+# We can use an "int" variable here.
+var col = 0
+for n in -99..100:
+  inc col
+  stdout.write &"{aDerivative(n):>4}"
+  stdout.write if col == 10: '\n' else: ' '
+  if col == 10: col = 0
+
+
+### Stretch task ###
+
+echo()
+
+# To avoid overflow, we have to use an "Integer" variable.
+var n = Integer(1)
+for m in 1..20:
+  n *= 10
+  let a = aDerivative(n)
+  let left = &"D(10^{m}) / 7"
+  echo &"{left:>12} = {a div 7}"

Task/Arithmetic-derivative/Perl/arithmetic-derivative.pl

@@ -0,0 +1,17 @@
+use v5.36;
+use bigint;
+no warnings 'uninitialized';
+use List::Util 'max';
+use ntheory 'factor';
+
+sub table ($c, @V) { my $t = $c * (my $w = 2 + length max @V); ( sprintf( ('%'.$w.'d')x@V, @V) ) =~ s/.{1,$t}\K/\n/gr }
+
+sub D ($n) {
+    my(%f, $s);
+    $f{$_}++ for factor max 1, my $nabs = abs $n;
+    map { $s += $nabs * $f{$_} / $_ } keys %f;
+    $n > 0 ? $s : -$s;
+}
+
+say table 10, map { D $_ } -99 .. 100;
+say join "\n", map { sprintf('D(10**%-2d) / 7 == ', $_) . D(10**$_) / 7 } 1 .. 20;

Task/Arithmetic-derivative/Phix/arithmetic-derivative.phix

@@ -0,0 +1,42 @@
+(phixonline)-->
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
+ <span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
+ <span style="color: #008080;">procedure</span> <span style="color: #000000;">D</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
+     <span style="color: #004080;">integer</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">mpz_neg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp_si</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: #000000;">0</span> <span style="color: #008080;">then</span>
+         <span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">else</span>
+         <span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_prime_factors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
+         <span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">vslice</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)),</span>
+                 <span style="color: #000000;">f1</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
+         <span style="color: #008080;">if</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
+             <span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+         <span style="color: #008080;">elsif</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
+             <span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f1</span> <span style="color: #0000FF;">+</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span><span style="color: #0000FF;">?</span><span style="color: #000000;">f1</span><span style="color: #0000FF;">:</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]))</span>
+         <span style="color: #008080;">else</span>
+             <span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f1</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
+             <span style="color: #004080;">mpz</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
+             <span style="color: #000000;">D</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
+             <span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f1</span><span style="color: #0000FF;">)</span>
+             <span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">d</span><span style="color: #0000FF;">)</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+         <span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #7060A8;">mpz_neg</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</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;">end</span> <span style="color: #008080;">procedure</span>
+
+ <span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">200</span><span style="color: #0000FF;">)</span>
+ <span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
+ <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">99</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</span> <span style="color: #008080;">do</span>
+     <span style="color: #7060A8;">mpz_set_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000000;">D</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">100</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">for</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;">"%s\n\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">:=</span><span style="color: #008000;">"%4s"</span><span style="color: #0000FF;">)})</span>
+ <span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">20</span> <span style="color: #008080;">do</span>
+     <span style="color: #7060A8;">mpz_ui_pow_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</span><span style="color: #0000FF;">)</span>
+     <span style="color: #000000;">D</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
+     <span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</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;">"D(10^%d)/7 = %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">m</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)})</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+<!--

Task/Arithmetic-derivative/Python/arithmetic-derivative.py

@@ -0,0 +1,19 @@
+from sympy.ntheory import factorint
+
+def D(n):
+    if n < 0:
+        return -D(-n)
+    elif n < 2:
+        return 0
+    else:
+        fdict = factorint(n)
+        if len(fdict) == 1 and 1 in fdict: # is prime
+            return 1
+        return sum([n * e // p for p, e in fdict.items()])
+
+for n in range(-99, 101):
+    print('{:5}'.format(D(n)), end='\n' if n % 10 == 0 else '')
+
+print()
+for m in range(1, 21):
+    print('(D for 10**{}) divided by 7 is {}'.format(m, D(10 ** m) // 7))

Task/Arithmetic-derivative/Quackery/arithmetic-derivative.quackery

@@ -0,0 +1,13 @@
+  [ dup 0 < iff
+      [ negate
+        ' negate ]
+    else []
+    swap 0 over
+    primefactors
+    witheach
+      [ dip over / + ]
+    nip swap do ]      is d ( n --> n )
+
+  200 times [ i^ 99 - d echo sp ]
+  cr cr
+  20 times [ 10 i^ 1+ ** d 7 / echo cr ]

Task/Arithmetic-derivative/Raku/arithmetic-derivative.raku

@@ -0,0 +1,14 @@
+use Prime::Factor;
+
+multi D (0) { 0 }
+multi D (1) { 0 }
+multi D ($n where &is-prime) { 1 }
+multi D ($n where * < 0 ) { -D -$n }
+multi D ($n) { sum $n.&prime-factors.Bag.map: { $n × .value / .key } }
+
+
+put (-99 .. 100).map(&D).batch(10)».fmt("%4d").join: "\n";
+
+put '';
+
+put join "\n", (1..20).map: { sprintf "D(10**%-2d) / 7 == %d", $_, D(10**$_) / 7 }

Task/Arithmetic-derivative/Wren/arithmetic-derivative.wren

@@ -0,0 +1,21 @@
+import "./big" for BigInt
+import "./fmt" for Fmt
+
+var D = Fn.new { |n|
+    if (n < 0) return -D.call(-n)
+    if (n < 2) return BigInt.zero
+    var f = BigInt.primeFactors(n)
+    var c = f.count
+    if (c == 1) return BigInt.one
+    if (c == 2) return f[0] + f[1]
+    var d = n / f[0]
+    return D.call(d) * f[0] + d
+}
+
+var ad = List.filled(200, 0)
+for (n in -99..100) ad[n+99] = D.call(BigInt.new(n))
+Fmt.tprint("$4i", ad, 10)
+System.print()
+for (m in 1..20) {
+    Fmt.print("D(10^$-2d) / 7 = $i", m, D.call(BigInt.ten.pow(m))/7)
+}