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A362133 Smallest indices k where A362131(k) = A362132(n).

%I A362133 #4 Apr 13 2023 14:07:58
%S A362133 1,3,5,7,9,12,17,31,36,41,58,74,82,112,160,189,198,220,294,325,914,
%T A362133 1267,1389,1872,1927,1957,2032,2155,2184,2302,2358,2835,3047,3672,
%U A362133 3794,3832,3873,3924,4543,4785,35502,98365,1728198,8375015
%N A362133 Smallest indices k where A362131(k) = A362132(n).
%C A362133 Next term exceeds 2^28, if it exists.
%H A362133 Michael De Vlieger, <a href="https://oeis.org/A362132/a362132.png">Plot (log_2 a(n), A362132(n)) at (x, y)</a>.
%t A362133 nn = 2^20;
%t A362133 c[_] := False; q[_] := False; h[_] := 0; f[n_] := DivisorSigma[0, n];
%t A362133 a[1] = j = u = w = 1;
%t A362133 {1}~Join~Rest@ Reap[Do[
%t A362133       If[c[j],
%t A362133         k = j + f[u]; h[j]++; h[u]--,
%t A362133         k = f[j]; c[j] = True; h[j]++ ];
%t A362133       u = Min[u, j]; Set[{a[n], q[k], j}, {k, True, k}];
%t A362133       While[h[u] == 0, u++];
%t A362133       If[k == w, While[q[w], w++]; Sow[n]], {n, 2, nn}] ][[-1, -1]]
%Y A362133 Cf. A360179, A362131, A362132.
%K A362133 nonn,more
%O A362133 1,2
%A A362133 _Michael De Vlieger_, Apr 10 2023