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A366124
The number of distinct prime factors of the largest unitary divisor of n that is a cube (A366126).
3
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
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]));
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Sep 30 2023
STATUS
approved