A260235 Number of distinct prime factors of the n-th hexagonal number (A000384).

2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3, 4, 2, 4, 3, 3, 3, 3, 2, 4, 2, 4, 3, 4, 2, 3, 4, 3, 4, 3, 2, 4, 4, 3, 2, 4, 3, 4, 3, 4, 3, 4, 2, 4, 3, 3, 4, 3, 3, 4, 3, 4, 3, 5, 2, 4, 3, 2, 4, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 3, 4, 5, 2, 4, 3, 3, 4, 4, 3, 4, 3

Offset: 2

Author

Colin Barker, Jul 20 2015

Keywords

• nonn

Examples

			a(6) = 3 because A000384(6) = 66 = 2 * 3 * 11.
		

Links

• Colin Barker, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A000384, A001221, A260233, A260234, A260236.

Programs

Mathematica

PrimeNu[PolygonalNumber[6,Range[2,90]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 23 2017 *)

PARI

pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
a(n) = omega(pg(6, n))

Formula

a(n) = A001221(A000384(n)).