new file: Math/powerfree_divisors.sf

Author: trizen

Math/continued_fraction_factorization_method.sf

@@ -75,7 +75,7 @@ func check_factor (n, g, factors) {
 func next_multiplier (k) {
     k += 2
 
-    while (!k.is_square_free) {
+    while (!k.is_squarefree) {
         ++k
     }
 

Math/digamma_function.sf

@@ -1,11 +1,10 @@
 #!/usr/bin/ruby
 
 # Daniel "Trizen" Șuteu
-# License: GPLv3
 # Date: 14 December 2016
 # https://github.com/trizen
 
-# Implementation for the digamma(n) function.
+# Simple implementation of the digamma(n) function.
 
 # See also:
 #   https://en.wikipedia.org/wiki/Digamma_function
@@ -18,4 +17,11 @@ func digamma(n) {
     })
 }
 
-say digamma(100)    #=> 4.60016185273808740019860558557585072686681279076853
+func digamma_from_harmonic(n) {
+    -γ + ::sum(1 ..^ n, { |k|
+        1/k
+    })
+}
+
+say digamma(100)                  #=> 4.60016185273808740019860558557585072686681279076853
+say digamma_from_harmonic(100)    #=> 4.60016185273808740019860558557585072686681279076853

Math/farey_factorization_method.sf

@@ -65,7 +65,7 @@ func check_factor (n, g, factors) {
 func next_multiplier (k) {
     k += 2
 
-    while (!k.is_square_free) {
+    while (!k.is_squarefree) {
         ++k
     }
 

Math/is_prob_squarefree.sf

@@ -54,7 +54,7 @@ func find_random_factor(n, small=true, trial=false) {
 func is_prob_squarefree(r, tries=50) {
 
     if (r.len <= 50) {
-        return r.is_square_free
+        return r.is_squarefree
     }
 
     return false if r.is_power
@@ -79,7 +79,7 @@ func is_prob_squarefree(r, tries=50) {
         var len = r.len
 
         if (len <= 50) {
-            return r.is_square_free
+            return r.is_squarefree
         }
 
         if (len <= 10_000) {
@@ -97,7 +97,7 @@ func is_prob_squarefree(r, tries=50) {
                 return false
             }
 
-            p.is_square_free || return false
+            p.is_squarefree || return false
 
             p.factor.each { |z|
                 if (z*z `divides` r) {

Math/powerfree_divisors.sf

@@ -0,0 +1,37 @@
+#!/usr/bin/ruby
+
+# Daniel "Trizen" Șuteu
+# Date: 05 October 2021
+# https://github.com/trizen
+
+# Generate all the k-powerfree divisors of n.
+
+func powerfree_divisors (n, k=2) {
+
+    var d  = [1]
+    var pp = n.factor_exp
+
+    for p,e in (pp) {
+
+        e = min(e, k-1)
+
+        var r = 1
+        d << gather {
+            e.times {
+                r *= p
+                d.each { |u|
+                    take(u*r)
+                }
+            }
+        }...
+    }
+
+    d.sort
+}
+
+say powerfree_divisors(5040, 2)
+say powerfree_divisors(5040, 3)
+
+__END__
+[1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210]
+[1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260]

README.md

@@ -444,6 +444,7 @@ A nice collection of day-to-day Sidef scripts.
     * [Pomerance condition for bpsw counter-example](./Math/pomerance_condition_for_bpsw_counter-example.sf)
     * [Power of 2 plus 3 primes lucas-lehmer](./Math/power_of_2_plus_3_primes_lucas-lehmer.sf)
     * [Power of 2 plus 5 primes lucas-lehmer](./Math/power_of_2_plus_5_primes_lucas-lehmer.sf)
+    * [Powerfree divisors](./Math/powerfree_divisors.sf)
     * [Primality precheck](./Math/primality_precheck.sf)
     * [Primality testing fermat fourier](./Math/primality_testing_fermat_fourier.sf)
     * [Primality testing wilson fourier](./Math/primality_testing_wilson_fourier.sf)