login
A368713
The maximal exponent in the prime factorization of the nonsquarefree numbers.
6
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
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
Similar sequences: A368710, A368711, A368712.
Sequence in context: A295312 A212174 A375342 * A375341 A368039 A160558
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jan 04 2024
STATUS
approved