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A283764 a(0) = 0; a(1) = 1; a(2*n) = sigma(a(n)), a(2*n+1) = sigma(a(n)+a(n+1)).

%I A283764 #8 Mar 16 2017 22:44:49
%S A283764 0,1,1,3,1,7,4,7,1,15,8,12,7,12,8,15,1,31,24,24,15,42,28,20,8,20,28,
%T A283764 42,15,24,24,31,1,63,32,72,60,124,60,56,24,80,96,144,56,124,42,56,15,
%U A283764 56,42,124,56,144,96,80,24,56,60,124,60,72,32,63,1,127,104,120,63,210,195,336,168,360,224,360,168,210,120,186,60,210,186,372,252,744,403,465,120,546
%N A283764 a(0) = 0; a(1) = 1; a(2*n) = sigma(a(n)), a(2*n+1) = sigma(a(n)+a(n+1)).
%C A283764 A variation on Stern's diatomic sequence (A002487) and iterating the sum of the divisors function (A007497).
%H A283764 Michael Gilleland, <a href="/selfsimilar.html">Some Self-Similar Integer Sequences</a>
%H A283764 Ilya Gutkovskiy, <a href="/A283764/a283764.pdf">Extended graphical example</a>
%H A283764 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A283764 a[0] = 0; a[1] = 1; a[n_] := If[EvenQ[n], DivisorSigma[1, a[n/2]], DivisorSigma[1, a[(n - 1)/2] + a[(n + 1)/2]]]; Table[a[n], {n, 0, 100}]
%o A283764 (PARI) a(n) = if(n<2, n, if(Mod(n,2), sigma(a((n - 1)/2) + a((n + 1)/2)), sigma(a(n/2))));
%o A283764 for(n=0, 100, print1(a(n),", ")) \\ _Indranil Ghosh_, Mar 16 2017
%Y A283764 Cf. A000203, A002487, A007497, A283166.
%K A283764 nonn
%O A283764 0,4
%A A283764 _Ilya Gutkovskiy_, Mar 16 2017