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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)