A283167 - OEIS

%I #13 Mar 22 2017 10:30:12

%S 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,

%T 32,31,30,24,28,24,16,15,24,28,24,28,16,15,14,8,16,15,14,8,12,12,8,7,

%U 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

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

%H Indranil Ghosh, <a href="/A283167/b283167.txt">Table of n, a(n) for n = 0..10000</a>

%H Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>

%H Ilya Gutkovskiy, <a href="/A283167/a283167.pdf">Extended graphical example</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

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

%e a(0) = 1;

%e a(1) = a(2*0+1) = sigma(a(0)) = sigma(1) = 1;

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

%e a(3) = a(2*1+1) = sigma(a(1)) = sigma(1) = 1;

%e a(4) = a(2*2) = 2*a(2) = 2*2 = 4;

%e a(5) = a(2*2+1) = sigma(a(2)) = sigma(2) = 1 + 2 = 3, etc.

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

%o (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

%Y Cf. A000203, A007497, A033879, A033880.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 02 2017