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A248410
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a(n) = number of polynomials a_k*x^k + ... + a_1*x + n with k > 0, integer coefficients and only distinct integer roots.
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3
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3, 11, 11, 23, 11, 43, 11, 47, 23, 43, 11, 103, 11, 43, 43, 83, 11, 103, 11, 103, 43, 43, 11, 223, 23, 43, 47, 103, 11, 187, 11, 139, 43, 43, 43, 275, 11, 43, 43, 223, 11, 187, 11, 103, 103, 43, 11, 427, 23, 103, 43, 103, 11, 223, 43, 223, 43, 43, 11, 503, 11, 43, 103, 227, 43, 187, 11, 103, 43, 187, 11, 635, 11, 43, 103, 103, 43, 187, 11
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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a(1)=3: x + 1; -x + 1; -x^2 + 1.
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PROG
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(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")
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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