A365710 a(n) = second smallest distinct prime factor of A126706(n).

3, 3, 5, 3, 7, 3, 5, 11, 5, 3, 5, 13, 3, 7, 3, 7, 17, 3, 5, 19, 5, 3, 11, 3, 23, 3, 7, 11, 5, 13, 3, 7, 29, 13, 3, 31, 3, 3, 5, 17, 5, 3, 7, 37, 3, 19, 17, 3, 5, 3, 41, 3, 19, 43, 7, 11, 3, 23, 47, 7, 3, 7, 3, 5, 3, 23, 13, 53, 3, 5, 7, 5, 3, 29, 3, 59, 3, 11

Offset: 1

Author

Michael De Vlieger, Jan 05 2024

Keywords

• nonn
• easy

Comments

Since omega(A126706(n)) = A001221(A126706(n)) > 1, and since A126706 is infinite, a(n) exists for all n.

Examples

			Let b(n) = A126706(n).
a(1) = 3 since b(1) = 12 = 2^2 * 3.
a(2) = 3 since b(2) = 18 = 2 * 3^2.
a(3) = 5 since b(3) = 20 = 2^2 * 5, etc.
		

Crossrefs

Cf. A119288, A126706.

Programs

Mathematica

FactorInteger[#][[2, 1]] & /@ Select[Range[250], PrimeOmega[#] > PrimeNu[#] > 1 &]

Formula

a(n) = A119288(A126706(n)) > 2.