A349049 Number of prime factors (with multiplicity) of the denominator of the harmonic number H(n) = Sum_{k=1..n} 1/k.

0, 1, 2, 3, 4, 3, 4, 5, 7, 7, 8, 8, 9, 9, 9, 10, 11, 10, 11, 10, 9, 9, 10, 11, 13, 13, 15, 15, 16, 16, 17, 18, 17, 17, 17, 17, 18, 18, 18, 18, 19, 18, 19, 20, 20, 20, 21, 21, 23, 23, 23, 23, 24, 23, 23, 23, 23, 23, 24, 24, 25, 25, 24, 25, 25, 24, 25, 25, 26, 26, 27, 28, 29, 29, 29, 29, 28

Offset: 1

Author

Kam Kong, Nov 07 2021

Keywords

• nonn

Crossrefs

Cf. A001222, A002805, A308967.

Programs

PARI

my(h=0); for(n=1,77,h+=1/n;print1(bigomega(denominator(h)),", ")); \\ Joerg Arndt, Nov 07 2021

Python

from sympy import harmonic, factorint
def a(n): return sum(factorint(harmonic(n).denominator).values())
print([a(n) for n in range(1, 78)]) # Michael S. Branicky, Nov 07 2021

SageMath

[sloane.A001222(A002805(n)) for n in range(1, 78)]

Formula

a(n) = A001222(A002805(n)).