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Smallest indices k where A362131(k) = A362132(n).
1

%I #4 Apr 13 2023 14:07:58

%S 1,3,5,7,9,12,17,31,36,41,58,74,82,112,160,189,198,220,294,325,914,

%T 1267,1389,1872,1927,1957,2032,2155,2184,2302,2358,2835,3047,3672,

%U 3794,3832,3873,3924,4543,4785,35502,98365,1728198,8375015

%N Smallest indices k where A362131(k) = A362132(n).

%C Next term exceeds 2^28, if it exists.

%H Michael De Vlieger, <a href="https://oeis.org/A362132/a362132.png">Plot (log_2 a(n), A362132(n)) at (x, y)</a>.

%t nn = 2^20;

%t c[_] := False; q[_] := False; h[_] := 0; f[n_] := DivisorSigma[0, n];

%t a[1] = j = u = w = 1;

%t {1}~Join~Rest@ Reap[Do[

%t If[c[j],

%t k = j + f[u]; h[j]++; h[u]--,

%t k = f[j]; c[j] = True; h[j]++ ];

%t u = Min[u, j]; Set[{a[n], q[k], j}, {k, True, k}];

%t While[h[u] == 0, u++];

%t If[k == w, While[q[w], w++]; Sow[n]], {n, 2, nn}] ][[-1, -1]]

%Y Cf. A360179, A362131, A362132.

%K nonn,more

%O 1,2

%A _Michael De Vlieger_, Apr 10 2023