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A375847
The maximum exponent in the prime factorization of the largest unitary cubefree divisor of n.
1
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, 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, 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
OFFSET
1,4
FORMULA
a(n) = A051903(A360539(n)).
a(n) = 0 if and only if n is cubefull (A036966).
a(n) = 1 if and only if n is in A337050 \ A036966.
a(n) = 2 if and only if n is in A038109.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 2 - A330596 = 1.25146474031763643535... .
MATHEMATICA
a[n_] := Max[Join[{0}, Select[FactorInteger[n][[;; , 2]], # <= 2 &]]]; a[1] = 0; Array[a, 100]
PROG
(PARI) a(n) = {my(e = select(x -> x <= 2, factor(n)[, 2])); if(#e == 0, 0, vecmax(e)); }
CROSSREFS
Cf. A007424 (analogous with the largest cubefree divisor, for n >= 2).
Sequence in context: A277045 A146061 A331186 * A372504 A135936 A109707
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Aug 31 2024
STATUS
approved