A248348 - OEIS

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).

%I #29 Nov 21 2014 16:05:54

%S 3,11,23,47,83,139,227,355,539,803,1175,1687,2391,3343,4619,6323,8571,

%T 11515,15355,20323,26715,34907,45339,58563,75263,96255,122535,155327,

%U 196087,246575,308931,385691,479899,595219,735979,907347,1115483,1367643,1672435

%N 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).

%C 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.

%H Hiroaki Yamanouchi, <a href="/A248348/b248348.txt">Table of n, a(n) for n = 0..1000</a>

%e a(0)= 3: x+1; -x+1; -x^2+1.

%Y Cf. A248410, A248956.

%K nonn

%O 0,1

%A _Reiner Moewald_, Oct 05 2014

%E a(15)-a(38) from _Hiroaki Yamanouchi_, Nov 21 2014