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A375847 The maximum exponent in the prime factorization of the largest unitary cubefree divisor of n.

%I A375847 #7 Aug 31 2024 15:16:24
%S A375847 0,1,1,2,1,1,1,0,2,1,1,2,1,1,1,0,1,2,1,2,1,1,1,1,2,1,0,2,1,1,1,0,1,1,
%T A375847 1,2,1,1,1,1,1,1,1,2,2,1,1,1,2,2,1,2,1,1,1,1,1,1,1,2,1,1,2,0,1,1,1,2,
%U A375847 1,1,1,2,1,1,2,2,1,1,1,1,0,1,1,2,1,1,1,1,1,2,1,2,1,1,1,1,1,2,2,2,1,1,1,1,1
%N A375847 The maximum exponent in the prime factorization of the largest unitary cubefree divisor of n.
%H A375847 Amiram Eldar, <a href="/A375847/b375847.txt">Table of n, a(n) for n = 1..10000</a>
%H A375847 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A375847 a(n) = A051903(A360539(n)).
%F A375847 a(n) = 0 if and only if n is cubefull (A036966).
%F A375847 a(n) = 1 if and only if n is in A337050 \ A036966.
%F A375847 a(n) = 2 if and only if n is in A038109.
%F A375847 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 - A330596 = 1.25146474031763643535... .
%t A375847 a[n_] := Max[Join[{0}, Select[FactorInteger[n][[;; , 2]], # <= 2 &]]]; a[1] = 0; Array[a, 100]
%o A375847 (PARI) a(n) = {my(e = select(x -> x <= 2, factor(n)[,2])); if(#e == 0, 0, vecmax(e));}
%Y A375847 Cf. A004709, A036966, A038109, A051903, A330596, A337050, A360539.
%Y A375847 Cf. A007424 (analogous with the largest cubefree divisor, for n >= 2).
%K A375847 nonn,easy
%O A375847 1,4
%A A375847 _Amiram Eldar_, Aug 31 2024