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A368925
The minimal exponent in the prime factorization of the powerful numbers.
1
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
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
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Feb 15 2024
STATUS
approved