A386468 The maximum exponent in the prime factorization of the largest exponentially squarefree divisor of n.

0, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 3, 3, 1, 1, 2, 1, 1, 1

Offset

1,4

Comments

First differs from A375428 at n = 64.

Differs from A368105 at n = 1, 36, 64, 72, 100, ... .

Except for a(1), all the terms are by definition squarefree numbers.

Links

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

Formula

a(n) = A051903(A365683(n)).

a(n) = A070321(A051903(n)) for n >= 2.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=2} A378085(k-1)*(1-1/zeta(k)) = 1.66055078443790141429... .

Mathematica

a[n_] := Module[{k = Max[FactorInteger[n][[;; , 2]]]}, While[! SquareFreeQ[k], k--]; k]; a[1] = 0; Array[a, 100]

Prog

(PARI) a(n) = if(n == 1, 0, my(k = vecmax(factor(n)[, 2])); while(!issquarefree(k), k--); k);

Crossrefs

Cf. A005117, A051903, A070321, A365683, A368105, A375428, A378085.

Sequence in context: A365552 A095691 A375428 * A368105 A182426 A371733

Adjacent sequences: A386465 A386466 A386467 * A386469 A386470 A386471

Keyword

nonn,easy

Author

Amiram Eldar, Jul 22 2025

Status

approved