A271319 - OEIS

%I #14 Sep 24 2023 14:54:04

%S 1,2,1,2,3,2,2,2,3,3,3,2,3,4,2,2,3,4,3,3,3,3,3,2,4,3,3,2,5,3,2,4,3,4,

%T 3,2,4,4,4,3,4,3,3,3,3,4,3,2,4,4,4,2,4,4,3,4,3,3,4,4,3,5,2,3,4,4,4,4,

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

%N Number of distinct prime factors of the n-th n-gonal number (A060354).

%H Colin Barker, <a href="/A271319/b271319.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n) = A001221(A060354(n)).

%e a(7) = 2 because A060354(7) = 112 = 2^4 * 7^1.

%t Table[PrimeNu[PolygonalNumber[n,n]],{n,2,90}] (* _Harvey P. Dale_, Sep 24 2023 *)

%o (PARI)

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

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

%o vector(100, n, n++; a(n))

%Y Cf. A001221, A060354, A271320, A271321, A271322.

%K nonn

%O 2,2

%A _Colin Barker_, Apr 04 2016