A260236 Number of prime factors, with multiplicity, of the n-th hexagonal number (A000384).

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

Offset: 2

Author

Colin Barker, Jul 20 2015

Keywords

• nonn

Examples

			a(4) = 3 because A000384(4) = 28 = 2^2 * 7.
		

Links

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

Crossrefs

Cf. A000384, A001222, A260233, A260234, A260235.

Programs

Mathematica

Rest[PrimeOmega[PolygonalNumber[6,Range[90]]]] (* Harvey P. Dale, Aug 10 2021 *)

PARI

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

Formula

a(n) = A001222(A000384(n)).