A359312 a(1) = 1; for n >= 1, a(2*n) = A000005(a(n)), a(2*n + 1) = A000005(a(n)) + 1.

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, 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, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2

Offset: 1

Author

Ctibor O. Zizka, Dec 25 2022

Keywords

• nonn

Examples

			a(1) = 1;
a(2) = A000005(a(1)) = 1;
a(3) = A000005(a(1)) + 1 = 2;
a(4) = A000005(a(2)) = 1;
a(5) = A000005(a(2)) + 1 = 2;
and so on.
		

Crossrefs

Cf. A000005, A131051.

Programs

Mathematica

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 *)

Formula

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

a(2^k) = 1.