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A375359
The maximum exponent in the prime factorization of the smallest number whose square is divisible by n.
2
0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1
OFFSET
1,8
COMMENTS
Differs from A050361 at n = 1, 64, 128, 192, ... . Differs from A366902 at n = 1, 64, 192, 216, ... . Differs from A325837 at n = 1, 216, 432, 648, ... .
FORMULA
a(n) = A051903(A019554(n)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum{k>=1} (1 - 1/zeta(2*k+1)) = 1.21464720975357037829... .
MATHEMATICA
a[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Max[(If[EvenQ[#], #, # + 1]) & /@ e]/2]; a[1] = 0; Array[a, 100]
PROG
(PARI) a(n) = if(n == 1, 0, vecmax(apply(x -> if(x % 2, x+1, x), factor(n)[, 2]))/2);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 13 2024
STATUS
approved