The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 30 05:42 EST 2023. Contains 367454 sequences. (Running on oeis4.)