From 6a97cdd3f19f07d5fb7e90c68ecb021979d0fe78 Mon Sep 17 00:00:00 2001
From: trizen <trizen@protonmail.com>
Date: Tue, 9 Nov 2021 20:04:09 +0200
Subject: [PATCH] - Added the Number `nesigma(n,k=1)` and `nesigma0(n)`
 methods.

Returns the sum and the count of the non-exponential divisors of n.

Example:

	say 30.of { .nesigma }      #=> OEIS: A160135
	say 30.of { .nesigma0 }     #=> OEIS: A160097
---
 lib/Sidef/Types/Number/Number.pm  | 10 ++++++++
 lib/Sidef/Types/Number/Number.pod | 38 +++++++++++++++++++++++--------
 2 files changed, 39 insertions(+), 9 deletions(-)

diff --git a/lib/Sidef/Types/Number/Number.pm b/lib/Sidef/Types/Number/Number.pm
index 73f81e84..a096266d 100644
--- a/lib/Sidef/Types/Number/Number.pm
+++ b/lib/Sidef/Types/Number/Number.pm
@@ -17125,6 +17125,16 @@ package Sidef::Types::Number::Number {
         bless \$s;
     }
 
+    sub nesigma0 {    # A160097: count of non-exponential divisors of n
+        my ($n) = @_;
+        $n->sigma0->sub($n->esigma0);
+    }
+
+    sub nesigma {     # A160135: sum of non-exponential divisors of n
+        my ($n, $k) = @_;
+        $n->sigma($k)->sub($n->esigma($k));
+    }
+
     sub uphi {
 
         # Multiplicative with:
diff --git a/lib/Sidef/Types/Number/Number.pod b/lib/Sidef/Types/Number/Number.pod
index 06ab14bd..6b7c0db1 100644
--- a/lib/Sidef/Types/Number/Number.pod
+++ b/lib/Sidef/Types/Number/Number.pod
@@ -1237,7 +1237,7 @@ Aliases: I<bsearch_inverse>
 
     bsigma(n, k=1)
 
-Returns the sum of the bi-unitary divisors of n, each divisor raised to power k.
+Returns the sum of the bi-unitary divisors of n, each divisor raised to the k-th power.
 
     say 20.of { .bsigma }   #=> OEIS: A188999
 
@@ -2267,7 +2267,7 @@ The complementary error function.
 
     esigma(n, k=1)
 
-Returns the sum of the exponential divisors (or e-divisors) of n.
+Returns the sum of the exponential divisors (or e-divisors) of n, each divisor raised to k-th power.
 
     say 20.of { .esigma }       #=> OEIS: A051377
 
@@ -3540,7 +3540,7 @@ Provided by L<Math::Prime::Util::GMP> >= 0.52.
 
     isigma(n, k=1)
 
-Returns the sum of the infinitary divisors of n, each divisor raised to power k.
+Returns the sum of the infinitary divisors of n, each divisor raised to the k-th power.
 
     say 20.of { .isigma }       #=> OEIS: A049417
 
@@ -4831,6 +4831,26 @@ Negates the sign of <Cx> (equivalent with: C<-x>).
 
 =cut
 
+=head2 nesigma
+
+    nesigma(n, k=1)
+
+Returns the sum of the non-exponential divisors of n, each divisor raised to the k-th power.
+
+    say 30.of { .nesigma }      #=> OEIS: A160135
+
+=cut
+
+=head2 nesigma0
+
+    nesigma0(n)
+
+Returns the count of the non-exponential divisors of n.
+
+    say 30.of { .nesigma0 }     #=> OEIS: A160097
+
+=cut
+
 =head2 new
 
     Number(string, base=10)
@@ -4931,7 +4951,7 @@ Returns the negative infinity special value (C<-Inf>).
 
     nisigma(n, k=1)
 
-Returns the sum of the non-infinitary divisors of n, each divisor raised to power k.
+Returns the sum of the non-infinitary divisors of n, each divisor raised to the k-th power.
 
     say 30.of { .nisigma }      #=> OEIS: A348271
 
@@ -5060,7 +5080,7 @@ Although this may or may not be actually faster.
 
     nusigma(n, k=1)
 
-Returns the sum of the non-unitary divisors of n, each divisor raised to power k.
+Returns the sum of the non-unitary divisors of n, each divisor raised to the k-th power.
 
     say 30.of { .nusigma }     #=> OEIS: A048146
 
@@ -5631,7 +5651,7 @@ Equivalent with:
 
     n.prime_power_sigma(k=1)
 
-Sum of the prime power divisors of n, each divisor raised to power k.
+Sum of the prime power divisors of n, each divisor raised to the k-th power.
 
 Example:
 
@@ -5707,7 +5727,7 @@ Returns an array with the prime numbers <= n, or in the range C<a..b>.
 
     n.prime_sigma(k=1)
 
-Sum of the unique prime divisors of n, each divisor raised to power k.
+Sum of the unique prime divisors of n, each divisor raised to the k-th power.
 
 Example:
 
@@ -5751,7 +5771,7 @@ Aliases: I<nth_prime_upper>
 
     n.prime_usigma(k=1)
 
-Sum of the unique unitary prime divisors of n, each divisor raised to power k.
+Sum of the unique unitary prime divisors of n, each divisor raised to the k-th power.
 
 Example:
 
@@ -6642,7 +6662,7 @@ Aliases: I<squarefree_unitary_divisors>, I<unitary_squarefree_divisors>
 
     n.squarefree_usigma(k=1)
 
-Sum of the unitary squarefree divisors of n, each divisor raised to power k.
+Sum of the unitary squarefree divisors of n, each divisor raised to the k-th power.
 
 Example: