A353347 -id:A353347 - cp's OEIS frontend

A353346 Numbers k such that the elements of the continued fraction of the abundancy index of k and k+1 are anagrams of each other.

2084564, 11784194, 13667268, 52820326, 68397891, 101183694, 128247668, 135641787, 137681487, 170542955, 266319572, 284966486, 384109196, 386860419, 482419526, 483785771, 546800667, 579468939, 606809224, 622241109, 703636544, 737703005, 829965829, 830993564, 834224684, 973986250

Offset: 1

Amiram Eldar, Apr 15 2022

nonn

			2084564 is a term since the sequences of elements of the continued fractions of sigma(2084564)/2084564 = 941472/521141 and sigma(2084565)/2084565 = 1270656/694855, {1, 1, 4, 5, 1, 8, 1, 5, 2, 4, 1, 7, 3} and {1, 1, 4, 1, 5, 8, 1, 2, 4, 7, 3, 1, 5} respectively, are anagrams of each other.

Amiram Eldar, Table of n, a(n) for n = 1..108

Cf. A000203 (sigma), A069567, A017665, A017666, A349685, A353345, A353347.

ab[n_] := Sort[ContinuedFraction[DivisorSigma[-1, n]]]; seq[max_] := Module[{s = {}, n = 2, c = 0, ab1 = ab[1], ab2}, While[n < max, ab2 = ab[n]; If[ab1 == ab2, AppendTo[s, n - 1]]; ab1 = ab2; n++]; s]; seq[1.4*10^7]

A353345 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.

Original entry on oeis.org

688126, 29900656, 35217656, 71624168, 154979487, 527560886, 871173148, 1370592266, 2461226804, 3232529461, 3232684430, 3431178214, 3471121856, 3486231973, 3527029430, 5732671200, 6258062402, 8784477355, 9334188311, 12670993089, 12707869077, 15120804392, 16317131894

Offset: 1

Amiram Eldar, Apr 15 2022

nonn

			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.

Cf. A069567, A099377, A099378, A349473, A353346, A353347.

Subsequence of A349499.

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]

cp's OEIS Frontend

A353346 Numbers k such that the elements of the continued fraction of the abundancy index of k and k+1 are anagrams of each other.

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