- Added several cube_* and cubefree_* aliases for 3.power_* and…

… `3.powerfree_`.

lib/Sidef/Types/Number/Number.pm

@@ -23929,6 +23929,10 @@ package Sidef::Types::Number::Number {
         (TWO)->powerfree_divisors($_[0]);
     }
 
+    sub cubefree_divisors {
+        (THREE)->powerfree_divisors($_[0]);
+    }
+
     my $power_divisors_func = sub {
         my ($k, $factor_exp) = @_;
 
@@ -24002,6 +24006,10 @@ package Sidef::Types::Number::Number {
         (TWO)->power_divisors($_[0]);
     }
 
+    sub cube_divisors {
+        (THREE)->power_divisors($_[0]);
+    }
+
     my $power_udivisors_func = sub {
         my ($k, $factor_exp) = @_;
 
@@ -24078,8 +24086,9 @@ package Sidef::Types::Number::Number {
         (TWO)->power_udivisors($_[0]);
     }
 
-    *unitary_square_divisors = \&square_udivisors;
-    *square_unitary_divisors = \&square_udivisors;
+    sub cube_udivisors {
+        (THREE)->power_udivisors($_[0]);
+    }
 
     sub powerfree_udivisors {
         my ($k, $n) = @_;
@@ -24128,15 +24137,13 @@ package Sidef::Types::Number::Number {
         Sidef::Types::Array::Array->new(\@d);
     }
 
-    *unitary_powerfree_divisors = \&powerfree_udivisors;
-    *powerfree_unitary_divisors = \&powerfree_udivisors;
-
     sub squarefree_udivisors {
         (TWO)->powerfree_udivisors($_[0]);
     }
 
-    *unitary_squarefree_divisors = \&squarefree_udivisors;
-    *squarefree_unitary_divisors = \&squarefree_udivisors;
+    sub cubefree_udivisors {
+        (THREE)->powerfree_udivisors($_[0]);
+    }
 
     sub prime_divisors {
         my $n = _big2pistr($_[0]) // return Sidef::Types::Array::Array->new();
@@ -25771,16 +25778,32 @@ package Sidef::Types::Number::Number {
         (TWO)->powerfree_usigma0($_[0]);
     }
 
+    sub cubefree_usigma0 {
+        (THREE)->powerfree_usigma0($_[0]);
+    }
+
     sub squarefree_usigma {
         (TWO)->powerfree_usigma($_[0], $_[1]);
     }
 
+    sub cubefree_usigma {
+        (THREE)->powerfree_usigma($_[0], $_[1]);
+    }
+
     *squarefree_sigma0 = \&usigma0;
 
+    sub cubefree_sigma0 {
+        (THREE)->powerfree_sigma0($_[0]);
+    }
+
     sub squarefree_sigma {
         (TWO)->powerfree_sigma($_[0], $_[1]);
     }
 
+    sub cubefree_sigma {
+        (THREE)->powerfree_sigma($_[0], $_[1]);
+    }
+
     sub power_sigma0 {
         my ($k, $n) = @_;
 
@@ -25862,6 +25885,14 @@ package Sidef::Types::Number::Number {
         (TWO)->power_sigma($_[0], $_[1]);
     }
 
+    sub cube_sigma0 {
+        (THREE)->power_sigma0($_[0]);
+    }
+
+    sub cube_sigma {
+        (THREE)->power_sigma($_[0], $_[1]);
+    }
+
     sub power_usigma0 {
         my ($k, $n) = @_;
 
@@ -25936,6 +25967,14 @@ package Sidef::Types::Number::Number {
         (TWO)->power_usigma($_[0], $_[1]);
     }
 
+    sub cube_usigma0 {
+        (THREE)->power_usigma0($_[0]);
+    }
+
+    sub cube_usigma {
+        (THREE)->power_usigma($_[0], $_[1]);
+    }
+
     sub powerfree_sigma0 {
         my ($k, $n) = @_;
 
@@ -29677,12 +29716,6 @@ package Sidef::Types::Number::Number {
         Math::GMPz::Rmpz_odd_p($n)             or return Sidef::Types::Bool::Bool::FALSE;
         Math::GMPz::Rmpz_cmp_ui($n, 1729) >= 0 or return Sidef::Types::Bool::Bool::FALSE;
 
-        # Must also be an Euler pseudoprime to base 2
-        if (!Math::GMPz::Rmpz_fits_ulong_p($n)) {
-            Math::Prime::Util::GMP::is_euler_pseudoprime(Math::GMPz::Rmpz_get_str($n, 10), 2)
-              || return Sidef::Types::Bool::Bool::FALSE;
-        }
-
         state $nm1   = Math::GMPz::Rmpz_init_nobless();
         state $nm1d2 = Math::GMPz::Rmpz_init_nobless();
         state $pm1   = Math::GMPz::Rmpz_init_nobless();
@@ -29703,6 +29736,12 @@ package Sidef::Types::Number::Number {
             }
         }
 
+        # Must also be an Euler pseudoprime to base 2
+        if (!Math::GMPz::Rmpz_fits_ulong_p($n)) {
+            Math::Prime::Util::GMP::is_euler_pseudoprime(Math::GMPz::Rmpz_get_str($n, 10), 2)
+              || return Sidef::Types::Bool::Bool::FALSE;
+        }
+
         # Check: p^((n-1)/2) == +/-1 (mod n), for random primes p
         foreach my $k (1 .. 7) {
             my $p = _random_prime(CORE::int(CORE::sqrt(ULONG_MAX)));

lib/Sidef/Types/Number/Number.pod

@@ -2004,6 +2004,20 @@ Returns the cube of C<x>. Equivalent with C<x**3>.
 
 =cut
 
+=head2 cube_divisors
+
+    n.cube_divisors
+
+Returns the cube divisors of C<n>.
+
+    say 10!.cube_divisors    #=> [1, 8, 27, 64, 216, 1728]
+
+Equivalent with:
+
+    n.divisors.grep { .is_cube }
+
+=cut
+
 =head2 cubefree
 
     cubefree(n)
@@ -2022,6 +2036,16 @@ Returns the count of cubefree numbers <= C<n>, or in the range C<a..b>.
 
 =cut
 
+=head2 cubefree_divisors
+
+    n.cubefree_divisors
+
+Returns an array with the cubefree divisors of C<n>.
+
+    say cubefree_divisors(120)  #=> [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]
+
+=cut
+
 =head2 cubefree_each
 
     n.cubefree_each { ... }
@@ -2033,6 +2057,25 @@ Aliases: I<each_cubefree>
 
 =cut
 
+=head2 cubefree_sigma
+
+    n.cubefree_sigma(k=1)
+
+Sum of the cubefree divisors of C<n>, each divisor raised to power C<k>.
+
+    say cubefree_sigma(5040)      #=> 4368
+    say cubefree_sigma(5040, 2)   #=> 2484300
+
+=cut
+
+=head2 cubefree_sigma0
+
+    n.cubefree_sigma0
+
+Returns the count of cubefree divisors of C<n>.
+
+=cut
+
 =head2 cubefree_sum
 
     cubefree_sum(n)
@@ -2042,6 +2085,37 @@ Returns the sum of cubefree numbers <= C<n>, or in the range C<a..b>.
 
 =cut
 
+=head2 cubefree_udivisors
+
+    n.cubefree_udivisors
+
+Returns the unitary cubefree divisors of C<n>.
+
+    say cubefree_udivisors(5040)   #=> [1, 5, 7, 9, 35, 45, 63, 315]
+
+=cut
+
+=head2 cubefree_usigma
+
+    n.cubefree_usigma(k=1)
+
+Sum of the unitary cubefree divisors of C<n>, each divisor raised to power C<k>.
+
+    say 5040.cubefree_usigma     #=> 480
+    say 5040.cubefree_usigma(2)  #=> 106600
+
+=cut
+
+=head2 cubefree_usigma0
+
+    n.cubefree_usigma0
+
+Returns the number of unitary cubefree divisors of C<n>.
+
+    say cubefree_usigma0(5040)    #=> 8
+
+=cut
+
 =head2 cubefull
 
     cubefull(n)
@@ -2080,6 +2154,62 @@ Returns the sum of cubefull numbers <= C<n>, or in the range C<a..b>.
 
 =cut
 
+=head2 cube_sigma
+
+    n.cube_sigma(k=1)
+
+Sum of the cube divisors of C<n>, each divisor raised to the power C<k>.
+
+    say 10!.cube_sigma       #=> 2044
+    say 10!.cube_sigma(2)    #=> 3037530
+
+Equivalent with:
+
+    n.cube_divisors.sum {|d| d**k }
+
+=cut
+
+=head2 cube_sigma0
+
+    n.cube_sigma0
+
+Returns the count of cube divisors of C<n>.
+
+=cut
+
+=head2 cube_udivisors
+
+    n.cube_udivisors
+
+Returns the unitary cube divisors of C<n>, such that each divisor C<d> is a cube and C<gcd(n/d, d) = 1>.
+
+    say 15!.cube_udivisors   #=> [1, 125, 729, 91125]
+
+=cut
+
+=head2 cube_usigma
+
+    n.cube_usigma(k=1)
+
+Sum of the unitary cube divisors of C<n>, each divisor raised to power C<k>.
+
+    say cube_usigma(15!)     #=> 91980
+    say cube_usigma(15!, 2)  #=> 8304312692
+
+Equivalent with:
+
+    n.cube_udivisors.sum {|d| d**k }
+
+=cut
+
+=head2 cube_usigma0
+
+    n.cube_usigma0
+
+Returns the count of unitary cube divisors of C<n>.
+
+=cut
+
 =head2 cubic_formula
 
     cubic_formula(a, b, c, d)
@@ -4589,8 +4719,8 @@ Aliases: I<is_positive>
 
 Returns true when all the exponents in the prime-power factorization of C<n> are less than C<k>.
 
-    say 15.by { .is_powerfree(2) }      # square-free numbers
-    say 15.by { .is_powerfree(3) }      # cube-free numbers
+    say 15.by { .is_powerfree(2) }      # squarefree numbers
+    say 15.by { .is_powerfree(3) }      # cubefree numbers
 
 =cut
 
@@ -6729,8 +6859,6 @@ Equivalent with (but much faster):
     n.udivisors.grep { .is_powerfree(k) }
     k.powerfree_divisors(n).grep {|d| gcd(n/d, d) == 1 }
 
-Aliases: I<powerfree_unitary_divisors>, I<unitary_powerfree_divisors>
-
 =cut
 
 =head2 powerfree_usigma
@@ -8313,7 +8441,7 @@ Aliases: I<square_free_count>
 
     squarefree_divisors(n)
 
-Returns an array with the square-free divisors of C<n>.
+Returns an array with the squarefree divisors of C<n>.
 
     say squarefree_divisors(120)  #=> [1, 2, 3, 5, 6, 10, 15, 30]
 
@@ -8385,7 +8513,7 @@ Aliases: I<squarefree_semiprimes_sum>
 
     squarefree_sigma(n,k=1)
 
-Sum of the square free divisors of C<n>, each divisor raised to power C<k>.
+Sum of the squarefree divisors of C<n>, each divisor raised to power C<k>.
 
     say squarefree_sigma(5040)      #=> 576
     say squarefree_sigma(5040, 2)   #=> 65000
@@ -8424,15 +8552,13 @@ Returns the unitary squarefree divisors of C<n>.
 
     say squarefree_udivisors(5040)   #=> [1, 5, 7, 35]
 
-Aliases: I<squarefree_unitary_divisors>, I<unitary_squarefree_divisors>
-
 =cut
 
 =head2 squarefree_usigma
 
     n.squarefree_usigma(k=1)
 
-Sum of the unitary squarefree divisors of C<n>, each divisor raised to the k-th power.
+Sum of the unitary squarefree divisors of C<n>, each divisor raised to power C<k>.
 
     say 5040.squarefree_usigma     #=> 48
     say 5040.squarefree_usigma(2)  #=> 1300
@@ -8521,8 +8647,6 @@ Returns the unitary square divisors of C<n>, such that each divisor C<d> is a sq
 
     say 5040.square_udivisors   #=> [1, 9, 16, 144]
 
-Aliases: I<square_unitary_divisors>, I<unitary_square_divisors>
-
 =cut
 
 =head2 square_usigma

scripts/Tests/divisor_functions.sf

@@ -9,13 +9,17 @@ var h = Hash(
     prime_divisors => 'prime_sigma',
     prime_power_divisors => 'prime_power_sigma',
     square_divisors => 'square_sigma',
+    cube_divisors => 'cube_sigma',
     squarefree_divisors => 'squarefree_sigma',
+    cubefree_divisors => 'cubefree_sigma',
 
     udivisors => 'usigma',
     prime_udivisors => 'prime_usigma',
     prime_power_udivisors => 'prime_power_usigma',
     square_udivisors => 'square_usigma',
+    cube_udivisors => 'cube_usigma',
     squarefree_udivisors => 'squarefree_usigma',
+    cubefree_udivisors => 'cubefree_usigma',
 
     edivisors => 'esigma',
     idivisors => 'isigma',