A308967 Number of prime factors (with multiplicity) of the numerator A001008 of the harmonic number H(n) = Sum_{k=1..n} 1/k.

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

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..325

Formula

a(n) = A001222(A001008(n)).

Example

H(1) = 1 = 1/1, the numerator is the empty product, whence a(1) = 0.
H(2) = 1 + 1/2 = 3/2 and H(3) = 3/2 + 1/3 = 11/6, 3 and 11 are prime numbers, whence a(2) = a(3) = 1.
H(4) = 11/6 + 1/4 = 25/12, 25 = 5^2, whence a(4) = 2.

Mathematica

Table[PrimeOmega @ Numerator[HarmonicNumber[n]], {n, 30}] (* Amiram Eldar, Feb 24 2020 *)

Prog

(PARI) a(n)=bigomega(A001008(n))

Crossrefs

Cf. A001008, A001222.

Sequence in context: A362890 A306251 A364027 * A241844 A233864 A133232

Adjacent sequences: A308964 A308965 A308966 * A308968 A308969 A308970

Keyword

nonn

Author

M. F. Hasler, Jul 03 2019

Status

approved