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

1,1

Comments

The terms of A051903 that are larger than 1.

Links

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

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).

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]

Prog

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

Crossrefs

Cf. A013661, A013929, A033150, A051903.

Similar sequences: A368710, A368711, A368712.

Sequence in context: A174329 A295312 A212174 * A368039 A160558 A241019

Adjacent sequences: A368710 A368711 A368712 * A368714 A368715 A368716

Keyword

nonn,easy

Author

Amiram Eldar, Jan 04 2024

Status

approved