A283166 a(0) = 0; a(1) = 1; a(2*n) = sigma(a(n)), a(2*n+1) = sigma(a(n)) + sigma(a(n+1)).

0, 1, 1, 2, 1, 4, 3, 4, 1, 8, 7, 11, 4, 11, 7, 8, 1, 16, 15, 23, 8, 20, 12, 19, 7, 19, 12, 20, 8, 23, 15, 16, 1, 32, 31, 55, 24, 48, 24, 39, 15, 57, 42, 70, 28, 48, 20, 28, 8, 28, 20, 48, 28, 70, 42, 57, 15, 39, 24, 48, 24, 55, 31, 32, 1, 64, 63, 95, 32, 104, 72, 132, 60, 184, 124, 184, 60, 116, 56, 80, 24, 104, 80, 176, 96, 240, 144, 200, 56, 180, 124

Offset: 0

Author

Ilya Gutkovskiy, Mar 02 2017

Keywords

• nonn

Comments

A variation on Stern's diatomic sequence (A002487) and iterating the sum of the divisors function (A007497).

Examples

			a(0) = 0;
a(1) = 1;
a(2) = a(2*1) = sigma(a(1)) = sigma(1) = 1;
a(3) = a(2*1+1) = sigma(a(1)) + sigma(a(2)) = sigma(1) + sigma(1) = 1 + 1  = 2;
a(4) = a(2*2) = sigma(a(2)) =  sigma(1) = 1;
a(5) = a(2*2+1) = sigma(a(2)) + sigma(a(3)) =  sigma(1) + sigma(2) = 1 + 3 = 4, etc.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..10000
• Michael Gilleland, Some Self-Similar Integer Sequences
• Ilya Gutkovskiy, Extended graphical example
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A002487, A007497.

Programs

Mathematica

a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], DivisorSigma[1, a[n/2]], DivisorSigma[1, a[(n - 1)/2]] + DivisorSigma[1, a[(n + 1)/2]]]; Table[a[n], {n, 0, 90}]

PARI

a(n) = if (n<2, n, if (n%2==0, sigma(a(n/2)), sigma(a((n-1)/2))+sigma(a((n+1)/2))));
tabl(nn)={for (n=0, nn, print1(a(n), ", "); ); };
tabl(90); \\ Indranil Ghosh, Mar 03 2017