A271320 Number of prime factors, with multiplicity, of the n-th n-gonal number (A060354).

1, 2, 4, 2, 3, 5, 5, 3, 3, 3, 7, 2, 3, 5, 6, 3, 4, 4, 6, 3, 3, 5, 6, 3, 4, 5, 9, 2, 5, 4, 7, 4, 4, 4, 7, 2, 4, 9, 7, 3, 4, 3, 7, 4, 3, 5, 7, 3, 5, 4, 7, 2, 6, 6, 6, 4, 3, 3, 9, 4, 3, 7, 8, 3, 4, 4, 7, 4, 4, 6, 8, 2, 4, 6, 7, 3, 4, 4, 8, 6, 4, 4, 8, 4, 3, 6

Offset: 2

Author

Colin Barker, Apr 04 2016

Keywords

• nonn

Examples

			a(7) = 5 because A060354(7) = 112 = 2^4 * 7^1.
		

Links

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

Crossrefs

Cf. A001222, A060354, A271319, A271321, A271322.

Programs

Mathematica

PrimeOmega/@Table[PolygonalNumber[n,n],{n,90}] (* Harvey P. Dale, Feb 08 2025 *)

PARI

pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
a(n) = bigomega(pg(n, n))
vector(100, n, n++; a(n))

Formula

a(n) = A001222(A060354(n)).