A366124 The number of distinct prime factors of the largest unitary divisor of n that is a cube (A366126).

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1

Comments

First differs from A295883, A318673 and A359472 at n = 64.

The number of exponents that are divisible by 3 in the prime factorization of n.

Links

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

Formula

a(n) = A001221(A366126(n)).

a(n) >= A295883(n).

a(n^3) = A001221(n).

Additive with a(p^e) = A079978(e).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} 1/(p^3+p^2+p) = 0.10770743252352371604... .

Mathematica

f[p_, e_] := If[Divisible[e, 3], 1, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = vecsum(apply(x -> if(!(x%3), 1, 0), factor(n)[, 2]));

Crossrefs

Cf. A001221, A079978, A162641, A366125, A366126.

Cf. A295883, A318673, A359472.

Sequence in context: A185017 A359472 A295883 * A295662 A367512 A187946

Adjacent sequences: A366121 A366122 A366123 * A366125 A366126 A366127

Keyword

nonn,easy

Author

Amiram Eldar, Sep 30 2023

Status

approved