A386472 The maximum exponent in the prime factorization of the largest divisor of n whose exponents in its prime factorization are squares.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1, 1

Offset

1,16

Comments

All the terms are by definition squares.

Links

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

Formula

a(n) = A051903(A386469(n)).

a(n) = A048760(A051903(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=1} (2*k+1)*(1-1/zeta((k+1)^2)) = 1.2383138701540899647042996... .

Mathematica

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

Prog

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

Crossrefs

Cf. A048760, A051903, A386469.

Sequence in context: A368474 A369935 A374325 * A368169 A367418 A360164

Adjacent sequences: A386469 A386470 A386471 * A386473 A386474 A386475

Keyword

nonn,easy

Author

Amiram Eldar, Jul 23 2025

Status

approved