A368925 The minimal exponent in the prime factorization of the powerful numbers.

0, 2, 3, 2, 4, 2, 3, 5, 2, 2, 6, 2, 4, 2, 2, 2, 3, 7, 2, 2, 2, 2, 3, 2, 5, 8, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 9, 2, 2, 4, 3, 2, 2, 6, 2, 2, 2, 3, 2, 2, 2, 2, 3, 10, 2, 2, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 11, 2, 7, 3, 2, 2, 2, 4

Offset

1,2

Links

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

Formula

a(n) = A051904(A001694(n)).

a(n) >= 2 for n >= 2.

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

Mathematica

s[n_] := If[n == 1, 0, Min @@ Last /@ FactorInteger[n]]; s /@ Select[Range[3000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]
(* or *)
f[n_] := Module[{e = Min[FactorInteger[n][[;; , 2]]]}, If[n == 1, 0, If[e > 1, e, Nothing]]]; Array[f, 3000]

Prog

(PARI) lista(kmax) = {my(e); for(k = 1, kmax, if(k == 1, print1(0, ", "), e = vecmin(factor(k)[, 2]); if(e > 1, print1(e, ", ")))); }

Crossrefs

Cf. A001694, A051904, A368710.

Sequence in context: A085058 A183152 A210942 * A368710 A080771 A025477

Adjacent sequences: A368922 A368923 A368924 * A368926 A368927 A368928

Keyword

nonn,easy

Author

Amiram Eldar, Feb 15 2024

Status

approved