A392281 - OEIS

%I #11 Jan 19 2026 15:46:46

%S 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,

%T 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,

%U 0,0,2,0,0,1,1,0,0,0,2,2,0,0,1,0,0,0,2,0,1

%N a(n) = log_2(A392280(n)).

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

%H Amiram Eldar, <a href="/A392281/b392281.txt">Table of n, a(n) for n = 2..10000</a>

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

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

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

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

%o (PARI) s(n) = {my(e = logint(n, 2)); if(n == 1 << e, e, e+1);}

%o a(n) = if(n == 1, 0, s(vecmax(factor(n)[, 2])));

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

%K nonn,easy

%O 2,7

%A _Amiram Eldar_, Jan 06 2026