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

1,1

Comments

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

Links

Table of n, a(n) for n=1..78.

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A119288, A126706.

Sequence in context: A163167 A243729 A200810 * A114003 A219792 A029622

Adjacent sequences: A365707 A365708 A365709 * A365711 A365712 A365713

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 05 2024

Status

approved