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A262891 a(n) = A060990(A259934(n)); branching degree of node n in the infinite trunk of the tree generated by edge-relation A049820(child) = parent.

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%I A262891 #11 Nov 17 2016 11:51:45
%S A262891 2,1,3,1,1,4,1,2,1,3,1,2,2,4,2,1,1,3,1,2,3,1,2,3,2,2,3,4,2,2,1,1,1,2,
%T A262891 3,2,1,1,2,1,2,2,3,3,1,1,3,2,2,1,1,1,4,1,1,1,2,2,1,2,1,2,1,2,2,1,2,2,
%U A262891 1,3,2,1,1,1,1,1,1,3,2,2,1,2,2,1,1,2,2,2,2,2,1,1,2,1,2,2,1,3,2,2,4,2,2,2,3,2,2,3,2,1,2,2,1,3,2,2,3,1,2,3,2,2,1
%N A262891 a(n) = A060990(A259934(n)); branching degree of node n in the infinite trunk of the tree generated by edge-relation A049820(child) = parent.
%H A262891 Antti Karttunen, <a href="/A262891/b262891.txt">Table of n, a(n) for n = 0..10341</a>
%F A262891 a(n) = A060990(A259934(n)).
%t A262891 nMax = 122; seq0 = {0}; seq = {1}; K = 1; While[seq != seq0, Print["K = ", K]; NN = K*nMax; Clear[A, B, S]; S[_] = 0; For[n = NN + 1, n <= 2*NN, n++, k = n - DivisorSigma[0, n]; If[k <= NN, S[k] = S[k] + 1; B[k] = n]]; For[n = NN, n >= 3, n--, If[S[n] >= 1, k = n - DivisorSigma[0, n]; S[k] = S[k] + 1; B[k] = n]]; A[0] = 0; A[1] = 2; For[n = 2, True, n++, b = B[A[n - 1]]; If[b > NN || S[b] > 1, Break[]]; A[n] = b]; Clear[a0]; a0[_] = 0; Do[n = x - DivisorSigma[0, x]; a0[n]++, {x, 1, NN}]; a[n_] := a0[A[n]]; seq0 = seq; seq = Table[a[n], {n, 0, nMax}]; K = 2K]; A262891 = seq (* _Jean-François Alcover_, Nov 16 2016, after _Robert Israel_ for A259934 *)
%o A262891 (Scheme) (define (A262891 n) (A060990 (A259934 n)))
%Y A262891 Cf. A049820, A060990, A259934.
%Y A262891 Positions of ones: A262892.
%K A262891 nonn
%O A262891 0,1
%A A262891 _Antti Karttunen_, Oct 04 2015