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A248348 a(n) = number of polynomials a_k*x^k + ... + a_1*x + a_0 with k > 0, integer coefficients, only distinct integer roots, and a_0 = p^n (p is a prime). 3
3, 11, 23, 47, 83, 139, 227, 355, 539, 803, 1175, 1687, 2391, 3343, 4619, 6323, 8571, 11515, 15355, 20323, 26715, 34907, 45339, 58563, 75263, 96255, 122535, 155327, 196087, 246575, 308931, 385691, 479899, 595219, 735979, 907347, 1115483, 1367643, 1672435 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
If D_n = {-p^n, ..., -p^0, p^0, ..., p^n} is the set of all positive and negative divisors of p^n (p is a prime), then a(n) gives the number of all subsets of D_n for which the product of all their elements is a divisor of p^n.
LINKS
EXAMPLE
a(0)= 3: x+1; -x+1; -x^2+1.
CROSSREFS
Sequence in context: A107138 A145473 A335677 * A173078 A128928 A289888
KEYWORD
nonn
AUTHOR
Reiner Moewald, Oct 05 2014
EXTENSIONS
a(15)-a(38) from Hiroaki Yamanouchi, Nov 21 2014
STATUS
approved

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Last modified February 26 05:55 EST 2024. Contains 370335 sequences. (Running on oeis4.)