A283166 - OEIS

%I #10 Mar 03 2017 20:34:43

%S 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,

%T 23,15,16,1,32,31,55,24,48,24,39,15,57,42,70,28,48,20,28,8,28,20,48,

%U 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

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

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

%H Indranil Ghosh, <a href="/A283166/b283166.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="/A283166/a283166.pdf">Extended graphical example</a>

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

%e a(0) = 0;

%e a(1) = 1;

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

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

%e a(4) = a(2*2) = sigma(a(2)) =  sigma(1) = 1;

%e a(5) = a(2*2+1) = sigma(a(2)) + sigma(a(3)) =  sigma(1) + sigma(2) = 1 + 3 = 4, etc.

%t 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}]

%o (PARI)

%o a(n) = if (n<2, n, if (n%2==0, sigma(a(n/2)), sigma(a((n-1)/2))+sigma(a((n+1)/2))));

%o tabl(nn)={for (n=0, nn, print1(a(n), ", "); ); };

%o tabl(90); \\ _Indranil Ghosh_, Mar 03 2017

%Y Cf. A000203, A002487, A007497.

%K nonn

%O 0,4

%A _Ilya Gutkovskiy_, Mar 02 2017