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A375040
The maximum exponent in the prime factorization of 2*n.
2
1, 2, 1, 3, 1, 2, 1, 4, 2, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 2, 2, 3, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 2, 2, 1, 5, 2, 2, 1, 3, 1, 3, 1, 4, 1, 2, 1, 3, 1, 2, 2, 7, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 2, 3, 1, 2, 1, 5, 4, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 2, 3, 1, 2, 1, 4, 1
OFFSET
1,2
FORMULA
a(n) = A051903(2*n).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=2} (1 - (2^k-2)/((2^k-1)*zeta(k))) = 2.15062559388175538361... .
MATHEMATICA
a[n_] := Max[FactorInteger[2*n][[;; , 2]]]; Array[a, 100]
PROG
(PARI) a(n) = vecmax(factor(2*n)[, 2]);
CROSSREFS
Bisection of A051903.
Sequence in context: A344771 A339914 A242923 * A065704 A325565 A286552
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jul 28 2024
STATUS
approved