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A260236
Number of prime factors, with multiplicity, of the n-th hexagonal number (A000384).
4
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
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
KEYWORD
nonn
AUTHOR
Colin Barker, Jul 20 2015
STATUS
approved