A366125 - OEIS

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A366125

The number of prime factors of the cube root of the largest unitary divisor of n that is a cube (A366126), counted with multiplicity.

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

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OFFSET

1,64

COMMENTS

First differs from A295662 at n = 32, and from A295883, A318673, A359472 and A366124 at n = 64.

One third of the sum 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) = A001222(A366126(n))/3.

Additive with a(p^e) = A175676(e) = e if e is divisible by 3, and 0 otherwise.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} p^2*(p-1)/(p^3-1)^2 = 0.35687351842962928035... .