cp's OEIS Frontend

A375359 The maximum exponent in the prime factorization of the smallest number whose square is divisible by n.

%I A375359 #8 Aug 13 2024 09:10:51
%S A375359 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,
%T A375359 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,
%U A375359 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
%N A375359 The maximum exponent in the prime factorization of the smallest number whose square is divisible by n.
%C A375359 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, ... .
%H A375359 Amiram Eldar, <a href="/A375359/b375359.txt">Table of n, a(n) for n = 1..10000</a>
%H A375359 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A375359 a(n) = A051903(A019554(n)).
%F A375359 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... .
%t A375359 a[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Max[(If[EvenQ[#], #, # + 1]) & /@ e]/2]; a[1] = 0; Array[a, 100]
%o A375359 (PARI) a(n) = if(n == 1, 0, vecmax(apply(x -> if(x % 2, x+1, x), factor(n)[,2]))/2);
%Y A375359 Cf. A019554, A051903, A372602, A375360.
%Y A375359 Cf. A050361, A325837, A366902.
%K A375359 nonn,easy
%O A375359 1,8
%A A375359 _Amiram Eldar_, Aug 13 2024