A392275 The maximum exponent in the prime factorization of the smallest number whose cube is divisible by n.

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

Offset

1,16

Comments

Differs from A043289 at n = 1, 81, 128, 162, 225, ... .

Differs from A053164 at n = 1, 81, 128, 162, 243, ... .

Differs from A063775 at n = 1, 128, 384, 640, 896, ... .

Differs from A203640 at n = 1, 64, 81, 128, 144, ... .

Differs from A295658 at n = 1, 64, 81, 128, 162, ... .

Differs from A365333 at n = 1, 64, 192, 256, 320, ... .

Differs from A384914 at n = 1, 128, 384, 512, 640, ... .

Links

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

Formula

a(n) = A051903(A019555(n)).

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

a(n) = A008620(A051903(n)-1) for n >= 2.

a(n) = A051903(A053149(n))/3 (one third of the maximum exponent in the prime factorization of the smallest cube divisible by n).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum{k>=1} (1 - 1/zeta(3*k+1)) = 1.08547548920820378574... .

Mathematica

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

Prog

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

Crossrefs

Cf. A008620, A019555, A051903, A053149, A375359, A392276, A392277.

Cf. A043289, A053164, A063775, A203640, A295658, A365333, A384914.

Sequence in context: A203640 A043289 A384914 * A063775 A053164 A365333

Adjacent sequences: A392272 A392273 A392274 * A392276 A392277 A392278

Keyword

nonn,easy

Author

Amiram Eldar, Jan 06 2026

Status

approved