A389836 a(n) = log_2(A278908(n)).

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1

Offset

1,36

Comments

First differs from A056170 and A369165 at n = 64.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A007814(A278908(n)).

Additive with a(p^e) = omega(e) = A001221(e).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=2} (omega(k)-omega(k-1))*P(k) = 0.46170540478688372421..., where P(s) is the prime zeta function.

Mathematica

f[p_, e_] := PrimeNu[e]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = vecsum(apply(omega, factor(n)[, 2]));
(Python)
from sympy.functions.combinatorial.numbers import primenu, factorint
def A389836(n): return sum(map(primenu, factorint(n).values())) # Chai Wah Wu, Oct 18 2025

Crossrefs

Cf. A001221, A007814, A056170, A278908, A369165.

Sequence in context: A388974 A369165 A056170 * A248395 A059483 A067618

Adjacent sequences: A389833 A389834 A389835 * A389837 A389838 A389839

Keyword

nonn,easy

Author

Amiram Eldar, Oct 16 2025

Status

approved