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

2,1

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A348772 A106482 A301805 * A122462 A215406 A231717

Adjacent sequences: A260233 A260234 A260235 * A260237 A260238 A260239

Keyword

nonn

Author

Colin Barker, Jul 20 2015

Status

approved