login
A259652
Number of prime factors, with multiplicity, of the n-th pentagonal number (A000326).
4
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
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
KEYWORD
nonn
AUTHOR
Colin Barker, Jul 02 2015
STATUS
approved