A259652 Number of prime factors, with multiplicity, of the n-th pentagonal number (A000326).

0, 1, 3, 2, 2, 2, 3, 3, 3, 2, 5, 4, 2, 2, 4, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 7, 3, 2, 3, 3, 6, 4, 2, 5, 4, 3, 2, 4, 5, 2, 5, 7, 3, 4, 2, 4, 6, 3, 3, 5, 4, 2, 5, 4, 4, 4, 2, 5, 4, 3, 3, 5, 6, 3, 3, 5, 4, 3, 4, 3, 6, 2, 3, 8, 3, 4, 3, 3, 5, 6, 4, 4, 4, 3, 2

Offset

1,3

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Formula

a(n) = A001222(A000326(n)).

Example

a(3) = 3 because A000326(3) = 12 = 2 * 2 * 3.

Mathematica

Table[PrimeOmega[n*(3n-1)/2], {n, 100}] (* Harvey P. Dale, Jul 22 2015 *)

Prog

(PARI)
pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ n-th m-gonal number
a(n) = bigomega(pg(5, n))

Crossrefs

Cf. A000326, A001222, A259649, A259650, A259651.

Sequence in context: A302481 A306542 A335171 * A141070 A283469 A163751

Adjacent sequences: A259649 A259650 A259651 * A259653 A259654 A259655

Keyword

nonn

Author

Colin Barker, Jul 02 2015

Status

approved