cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A349476 Numbers k such that the continued fraction of the harmonic mean of the divisors of k contains a single distinct element.

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%I A349476 #11 Nov 21 2021 05:08:56
%S A349476 1,6,15,28,30,140,270,496,545,672,792,1365,1638,2970,3515,6200,8128,
%T A349476 8190,18600,18620,27846,30240,32760,44950,46359,55860,59670,105664,
%U A349476 117800,167400,173600,237510,242060,253539,332640,360360,539400,681156,691782,695520,726180,753480,950976
%N A349476 Numbers k such that the continued fraction of the harmonic mean of the divisors of k contains a single distinct element.
%C A349476 All the harmonic numbers (A001599) are terms of this sequence.
%C A349476 The least term with m elements in the continued fraction of the harmonic mean of its divisors for m = 1, 2, 3, and 4 is 1, 15, 792 and 545, respectively.
%C A349476 Are there terms with more than 4 elements? There are no such terms below 2*10^9.
%H A349476 Amiram Eldar, <a href="/A349476/b349476.txt">Table of n, a(n) for n = 1..150</a>
%e A349476 15 is a term since the harmonic mean of its divisors is 5/2 = 2 + 1/2.
%e A349476 545 is a term since the harmonic mean of its divisors is 109/33 = 3 + 1/(3 + 1/(3 + 1/3)).
%e A349476 792 is a term since the harmonic mean of its divisors is 528/65 = 8 + 1/(8 + 1/8).
%t A349476 c[n_] := ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[-1, n]]; q[n_] := Length[Union[c[n]]] == 1; Select[Range[10^6], q]
%Y A349476 Cf. A099377, A099378, A349473.
%K A349476 nonn
%O A349476 1,2
%A A349476 _Amiram Eldar_, Nov 19 2021