A248410 a(n) = number of polynomials a_k*x^k + ... + a_1*x + n with k > 0, integer coefficients and only distinct integer roots.

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

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

Cf. A248348, A248955.

Sequence in context: A080351 A178709 A168378 * A059200 A232038 A072980

Adjacent sequences: A248407 A248408 A248409 * A248411 A248412 A248413

Keyword

nonn

Author

Reiner Moewald, Oct 06 2014

Status

approved