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%I #13 Sep 19 2022 14:13:48
%S 688126,29900656,35217656,71624168,154979487,527560886,871173148,
%T 1370592266,2461226804,3232529461,3232684430,3431178214,3471121856,
%U 3486231973,3527029430,5732671200,6258062402,8784477355,9334188311,12670993089,12707869077,15120804392,16317131894
%N Numbers k such that the elements of the continued fractions of the harmonic means of the divisors of k and k+1 are anagrams of each other.
%e 688126 is a term since sequences of elements of the continued fractions of the harmonic means of the divisors of 688126 and 688127, 688126/70281 and 688127/77304, are {9, 1, 3, 1, 3, 1, 2, 9, 1, 1, 6, 8} and {8, 1, 9, 6, 3, 1, 2, 1, 3, 1, 1, 9} respectively, and they are anagrams of each other.
%t h[n_] := Sort[ContinuedFraction[DivisorSigma[0, n]/DivisorSigma[-1, n]]]; seq[max_] := Module[{s = {}, n = 2, c = 0, h1 = h[1], h2}, While[n < max, h2 = h[n]; If[h1 == h2, AppendTo[s, n - 1]]; h1 = h2; n++]; s]; seq[4*10^7]
%Y Cf. A069567, A099377, A099378, A349473, A353346, A353347.
%Y Subsequence of A349499.
%K nonn
%O 1,1
%A _Amiram Eldar_, Apr 15 2022