OFFSET
1,1
COMMENTS
If D_n is the set of all positive and negative divisors of n, then a(n) is the number of all subsets of D_n for which the product of all their elements is a divisor of n. a(n) depends only on the prime signature of n.
LINKS
Reiner Moewald, Table of n, a(n) for n = 1..502
EXAMPLE
a(1)=3: x + 1; -x + 1; -x^2 + 1.
PROG
(Python)
from itertools import chain, combinations
def powerset(iterable):
...s = list(iterable)
...return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
print("Start")
a_n = 0
for num in range(1, 1000):
...div_set = set((-1, 1))
...a_n = 0
...for divisor in range(1, num + 1):
......if (num % divisor == 0):
.........div_set.add(divisor)
.........div_set.add(divisor*(-1))
...pow_set = set(powerset(div_set))
...num_set = len(pow_set)
...for count_set in range(0, num_set):
......subset = set(pow_set.pop())
......num_subset = len(subset)
......prod = 1
......if num_subset < 1:
.........prod = 0
......for count_subset in range (0, num_subset):
.........prod = prod * subset.pop()
......if prod != 0:
.........if (num % prod == 0):
............a_n = a_n +1
...print(num, a_n)
print("Ende")
CROSSREFS
KEYWORD
nonn
AUTHOR
Reiner Moewald, Oct 06 2014
STATUS
approved