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, 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

Offset: 0

Author

Reiner Moewald, Oct 05 2014

Keywords

• nonn

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.

Examples

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

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A248410, A248956.

Extensions

a(15)-a(38) from Hiroaki Yamanouchi, Nov 21 2014