A375847 - OEIS

%I #7 Aug 31 2024 15:16:24

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

%H Amiram Eldar, <a href="/A375847/b375847.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F a(n) = A051903(A360539(n)).

%F a(n) = 0 if and only if n is cubefull (A036966).

%F a(n) = 1 if and only if n is in A337050 \ A036966.

%F a(n) = 2 if and only if n is in A038109.

%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 - A330596 = 1.25146474031763643535... .

%t a[n_] := Max[Join[{0}, Select[FactorInteger[n][[;; , 2]], # <= 2 &]]]; a[1] = 0; Array[a, 100]

%o (PARI) a(n) = {my(e = select(x -> x <= 2, factor(n)[,2])); if(#e == 0, 0, vecmax(e));}

%Y Cf. A004709, A036966, A038109, A051903, A330596, A337050, A360539.

%Y Cf. A007424 (analogous with the largest cubefree divisor, for n >= 2).

%K nonn,easy

%O 1,4

%A _Amiram Eldar_, Aug 31 2024