A392281 a(n) = log_2(A392280(n)).

0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 2, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 1, 3, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 2, 0, 1

Offset

2,7

Comments

Differs from A383104 at n = 64, 192, 320, 448, 512, ... .

Links

Amiram Eldar, Table of n, a(n) for n = 2..10000

Formula

a(n) = A007814(A051903(A356194(n))).

a(n) = A029837(A051903(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=2..m} a(k) = Sum_{k>=0} (1-1/zeta(2^k+1)) = 0.59779018966096834585... .

Mathematica

a[n_] := Ceiling[Log2[Max[FactorInteger[n][[;; , 2]]]]]; Array[a, 100, 2]

Prog

(PARI) s(n) = {my(e = logint(n, 2)); if(n == 1 << e, e, e+1); }
a(n) = if(n == 1, 0, s(vecmax(factor(n)[, 2])));

Crossrefs

Cf. A007814, A029837, A051903, A369934, A374328, A383104, A392280.

Sequence in context: A336352 A081221 A383104 * A366988 A280827 A103840

Adjacent sequences: A392278 A392279 A392280 * A392282 A392283 A392284

Keyword

nonn,easy

Author

Amiram Eldar, Jan 06 2026

Status

approved