A375040 The maximum exponent in the prime factorization of 2*n.

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

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n.

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.

Cf. A033150, A375039.

Sequence in context: A344771 A339914 A242923 * A065704 A325565 A286552

Adjacent sequences: A375037 A375038 A375039 * A375041 A375042 A375049

Keyword

nonn,easy

Author

Amiram Eldar, Jul 28 2024

Status

approved