A283167 a(0) = 1; a(2*n) = 2*a(n), a(2*n+1) = sigma(a(n)).

1, 1, 2, 1, 4, 3, 2, 1, 8, 7, 6, 4, 4, 3, 2, 1, 16, 15, 14, 8, 12, 12, 8, 7, 8, 7, 6, 4, 4, 3, 2, 1, 32, 31, 30, 24, 28, 24, 16, 15, 24, 28, 24, 28, 16, 15, 14, 8, 16, 15, 14, 8, 12, 12, 8, 7, 8, 7, 6, 4, 4, 3, 2, 1, 64, 63, 62, 32, 60, 72, 48, 60, 56, 56, 48, 60, 32, 31, 30, 24, 48, 60, 56, 56, 48, 60, 56, 56, 32, 31, 30

Offset: 0

Author

Ilya Gutkovskiy, Mar 02 2017

Keywords

• nonn

Examples

			a(0) = 1;
a(1) = a(2*0+1) = sigma(a(0)) = sigma(1) = 1;
a(2) = a(2*1) = 2*a(1) = 2*1 = 2;
a(3) = a(2*1+1) = sigma(a(1)) = sigma(1) = 1;
a(4) = a(2*2) = 2*a(2) = 2*2 = 4;
a(5) = a(2*2+1) = sigma(a(2)) = sigma(2) = 1 + 2 = 3, 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, A007497, A033879, A033880.

Programs

Mathematica

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

PARI

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

Formula

a(2*n) - a(2*n+1) = A033879(a(n)).

a(2*n+1) - a(2*n) = A033880(a(n)).