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

Author

Amiram Eldar, Jul 23 2025

Keywords

• nonn
• easy

Comments

All the terms are by definition squares.

Links

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

Crossrefs

Cf. A048760, A051903, A386469.

Programs

Mathematica

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

PARI

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

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... .