Weird and Semi-perfect numbers

sympy/ntheory/__init__.py

@@ -5,12 +5,14 @@
 from .generate import nextprime, prevprime, prime, primepi, primerange, \
     randprime, Sieve, sieve, primorial, cycle_length, composite, compositepi
 from .primetest import isprime
+
 from .factor_ import divisors, proper_divisors, factorint, multiplicity, \
     perfect_power, pollard_pm1, pollard_rho, primefactors, totient, trailing, \
     divisor_count, proper_divisor_count, divisor_sigma, factorrat, \
     reduced_totient, primenu, primeomega, mersenne_prime_exponent, \
     is_perfect, is_mersenne_prime, is_abundant, is_deficient, is_amicable, \
-    abundance
+    abundance, is_semiperfect, is_weird
+
 from .partitions_ import npartitions
 from .residue_ntheory import is_primitive_root, is_quad_residue, \
     legendre_symbol, jacobi_symbol, n_order, sqrt_mod, quadratic_residues, \
@@ -29,12 +31,14 @@
 
     'isprime',
 
+
     'divisors', 'proper_divisors', 'factorint', 'multiplicity', 'perfect_power',
     'pollard_pm1', 'pollard_rho', 'primefactors', 'totient', 'trailing',
     'divisor_count', 'proper_divisor_count', 'divisor_sigma', 'factorrat',
     'reduced_totient', 'primenu', 'primeomega', 'mersenne_prime_exponent',
     'is_perfect', 'is_mersenne_prime', 'is_abundant', 'is_deficient', 'is_amicable',
-    'abundance',
+    'abundance', 'is_semiperfect', 'is_weird',
+
 
     'npartitions',
 

sympy/ntheory/factor_.py

@@ -2371,3 +2371,64 @@ def is_amicable(m, n):
         return False
     a, b = map(lambda i: divisor_sigma(i), (m, n))
     return a == b == (m + n)
+
+
+def is_semiperfect(n):
+    """Returns True if the number 'n' is "semi-perfect", else returns False
+    Semiperfect number is a natural number that is equal to the sum of all
+    or some of its proper devisors
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import is_semiperfect
+    >>> is_semiperfect(40)
+    True
+    >>> is_semiperfect(38)
+    False
+
+    Reference
+    =========
+    .. [1] https://en.wikipedia.org/wiki/Semiperfect_number
+    """
+
+    factors = divisors(n)
+    factors = factors[:-1]
+    num_factors = len(factors)
+
+    subset = [[0 for i in range(n + 1)]for j in range(num_factors + 1)]
+    for i in range(num_factors + 1):
+        subset[i][0]= True
+    for i in range(1, n + 1):
+        subset[0][i] = False
+
+    for i in range(1, num_factors + 1):
+        for j in range(1, n + 1):
+            if j < factors[i - 1]:
+                subset[i][j] = subset[i - 1][j]
+            else:
+                subset[i][j] = subset[i - 1][j] or subset[i - 1][j - factors[i - 1]]
+    if subset[num_factors][n] == 0:
+        return False
+    return True
+
+
+def is_weird(n):
+    """Returns True if the number 'n' is "weird", else returns False
+    Weird number is a natural number taht is abundant but not semiperfect.
+    Examples
+    ========
+
+    >>> from sympy.ntheory.factor_ import is_weird
+    >>> is_weird(70)
+    True
+    >>> is_weird(50)
+    False
+
+    Reference
+    =========
+    .. [1] https://en.wikipedia.org/wiki/Weird_number
+    """
+
+    if is_abundant(n) == True and is_semiperfect(n) == False:
+        return True
+    return False

sympy/ntheory/tests/test_factor_.py

@@ -12,7 +12,7 @@
     antidivisors, antidivisor_count, core, digits, udivisors, udivisor_sigma,
     udivisor_count, proper_divisor_count, primenu, primeomega, small_trailing,
     mersenne_prime_exponent, is_perfect, is_mersenne_prime, is_abundant,
-    is_deficient, is_amicable)
+    is_deficient, is_amicable, is_semiperfect, is_weird)
 from sympy.ntheory.generate import cycle_length
 from sympy.ntheory.multinomial import (
     multinomial_coefficients, multinomial_coefficients_iterator)
@@ -658,3 +658,15 @@ def test_is_amicable():
     assert is_amicable(173, 129) is False
     assert is_amicable(220, 284) is True
     assert is_amicable(8756, 8756) is False
+
+
+def test_is_semiperfect():
+    assert is_semiperfect(260) is True
+    assert is_semiperfect(38) is False
+    assert is_semiperfect(70) is False
+
+
+def test_is_weird():
+    assert is_weird(13930) is True
+    assert is_weird(7192) is True
+    assert is_weird(100) is False