A359312 - OEIS

%I #20 Dec 31 2022 15:16:24

%S 1,1,2,1,2,2,3,1,2,2,3,2,3,2,3,1,2,2,3,2,3,2,3,2,3,2,3,2,3,2,3,1,2,2,

%T 3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,1,2,2,3,2,

%U 3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2,3,2

%N a(1) = 1; for n >= 1, a(2*n) = A000005(a(n)), a(2*n + 1) = A000005(a(n)) + 1.

%F Sum_{i = 2^k..2^(k + 1) - 1} a(i) = 5*2^(k - 1) - 2, for k >= 1.

%F a(2^k) = 1.

%e a(1) = 1;

%e a(2) = A000005(a(1)) = 1;

%e a(3) = A000005(a(1)) + 1 = 2;

%e a(4) = A000005(a(2)) = 1;

%e a(5) = A000005(a(2)) + 1 = 2;

%e and so on.

%t a[1] = 1; a[n_] := a[n] = If[EvenQ[n], DivisorSigma[0, a[n/2]], DivisorSigma[0, a[(n - 1)/2]] + 1]; Array[a, 100] (* _Amiram Eldar_, Dec 25 2022 *)

%Y Cf. A000005, A131051.

%K nonn

%O 1,3

%A _Ctibor O. Zizka_, Dec 25 2022