From 46a3ee723d4dbd4e22cf2e9400e5ce9ea9186b0a Mon Sep 17 00:00:00 2001
From: trizen <trizen@protonmail.com>
Date: Sat, 21 Aug 2021 02:13:24 +0300
Subject: [PATCH] - Added the Number `k.powerfree_part(n)` method.

Returns the k-powerfree part of `n`:

    say 30.of { 2.powerfree_part(_) }       # squarefree part (OEIS: A007913)
    say 30.of { 3.powerfree_part(_) }       # cubefree part (OEIS: A050985)
---
 lib/Sidef/Types/Number/Number.pm  | 24 ++++++++++++++++++++----
 lib/Sidef/Types/Number/Number.pod | 11 +++++++++++
 2 files changed, 31 insertions(+), 4 deletions(-)

diff --git a/lib/Sidef/Types/Number/Number.pm b/lib/Sidef/Types/Number/Number.pm
index 9c427be8..92923bf5 100644
--- a/lib/Sidef/Types/Number/Number.pm
+++ b/lib/Sidef/Types/Number/Number.pm
@@ -14170,20 +14170,36 @@ package Sidef::Types::Number::Number {
         _set_int($r);
     }
 
-    sub core {    # A007913
+    sub powerfree_part {
+        my ($k, $n) = @_;
 
         # Multiplicative with:
-        #   a(p^k) = p^(k mod 2)
+        #   a(p^e, k) = p^(e mod k)
 
-        my $n = &_big2uistr // goto &nan;
+        _valid(\$n);
+
+        $k = _any2ui($$k)   // goto &nan;
+        $n = _big2uistr($n) // goto &nan;
+
+        $k <= 0 and goto &nan;
 
         my @factor_exp = _factor_exp($n);
         @factor_exp and $factor_exp[0][0] eq '0' and return ZERO;
 
-        my $r = Math::Prime::Util::GMP::vecprod(map { $_->[0] } grep { $_->[1] % 2 } @factor_exp);
+        my $r = Math::Prime::Util::GMP::vecprod(
+            map {
+                ($_->[1] == 1)
+                  ? $_->[0]
+                  : Math::Prime::Util::GMP::powint($_->[0], $_->[1])
+              } grep { $_->[1] } map { [$_->[0], $_->[1] % $k] } @factor_exp
+        );
         _set_int($r);
     }
 
+    sub core {    # A007913
+        (TWO)->powerfree_part($_[0]);
+    }
+
     sub arithmetic_derivative {
         my ($x) = @_;
 
diff --git a/lib/Sidef/Types/Number/Number.pod b/lib/Sidef/Types/Number/Number.pod
index 894d7048..a9bb069a 100644
--- a/lib/Sidef/Types/Number/Number.pod
+++ b/lib/Sidef/Types/Number/Number.pod
@@ -5202,6 +5202,17 @@ It efficiently counts the number of k-powerfree numbers <= n, or in the range C<
 
 =cut
 
+=head2 powerfree_part
+
+    k.powerfree_part(n)
+
+Returns the k-powerfree part of C<n>.
+
+    say 30.of { 2.powerfree_part(_) }       # squarefree part (OEIS: A007913)
+    say 30.of { 3.powerfree_part(_) }       # cubefree part (OEIS: A050985)
+
+=cut
+
 =head2 powerfree_sum
 
     k.powerfree_sum(n)