A368713 The maximal exponent in the prime factorization of the nonsquarefree numbers.

2, 3, 2, 2, 4, 2, 2, 3, 2, 3, 2, 5, 2, 3, 2, 2, 4, 2, 2, 2, 3, 3, 2, 2, 6, 2, 3, 2, 2, 4, 4, 2, 3, 2, 2, 5, 2, 2, 2, 3, 3, 4, 2, 2, 3, 2, 2, 3, 2, 7, 2, 3, 3, 2, 4, 2, 2, 2, 3, 2, 2, 5, 4, 2, 3, 2, 2, 2, 2, 4, 2, 3, 2, 3, 6, 2, 2, 3, 2, 2, 4, 2, 3, 2, 5, 2, 2, 3, 2, 2, 4

Offset: 1

Author

Amiram Eldar, Jan 04 2024

Keywords

• nonn
• easy

Comments

The terms of A051903 that are larger than 1.

Links

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

Crossrefs

Cf. A013661, A013929, A033150, A051903.

Similar sequences: A368710, A368711, A368712.

Programs

Mathematica

s[n_] := Max @@ Last /@ FactorInteger[n]; s /@ Select[Range[250], !SquareFreeQ[#] &]
(* or *)
f[n_] := Module[{e = Max @@ FactorInteger[n][[;; , 2]]}, If[e > 1, e, Nothing]]; Array[f, 250]

PARI

lista(kmax) = {my(e); for(k = 2, kmax, e = vecmax(factor(k)[,2]); if(e > 1, print1(e, ", ")));}

Formula

a(n) = A051903(A013929(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (c * zeta(2) - 1)/(zeta(2) - 1) = 2.798673520766..., where c = 1.705211... is Niven's constant (A033150).