A260235 - OEIS

%I #7 Jun 23 2017 19:01:14

%S 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,

%T 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,

%U 4,3,4,3,4,3,3,4,5,2,4,3,3,4,4,3,4,3

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

%H Colin Barker, <a href="/A260235/b260235.txt">Table of n, a(n) for n = 2..1000</a>

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

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

%t PrimeNu[PolygonalNumber[6,Range[2,90]]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jun 23 2017 *)

%o (PARI)

%o pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number

%o a(n) = omega(pg(6, n))

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

%K nonn

%O 2,1

%A _Colin Barker_, Jul 20 2015