A392277 The maximum exponent in the prime factorization of the cube root of the largest cube dividing n.

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

Offset

1,64

Comments

Differs from A366123 at n = 216, 432, 648, 864, 1000, ... .

Differs from A295659 at n = 64, 128, 192, 216, 256, ... .

Links

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

Formula

a(n) = A051903(A053150(n)).

a(n) = floor(A051903(n)/3).

a(n) = A051903(A008834(n))/3 (one third of the maximum exponent in the prime factorization of the largest cube dividing n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} (1 - 1/zeta(3*k)) = 0.18742537806898429473... .

Mathematica

a[n_] := Floor[Max[FactorInteger[n][[;; , 2]]]/3]; a[1] = 0; Array[a, 100]

Prog

(PARI) a(n) = if(n == 1, 0, vecmax(factor(n)[, 2])\3);

Crossrefs

Cf. A008834, A051903, A053150, A295659, A366123, A375359, A392275, A392276.

Sequence in context: A318655 A056626 A366123 * A290081 A347706 A348381

Adjacent sequences: A392274 A392275 A392276 * A392278 A392279 A392280

Keyword

nonn,easy

Author

Amiram Eldar, Jan 06 2026

Status

approved