A349502 - OEIS

%I #8 Nov 21 2021 05:08:33

%S 1,2,3,6,9,14,20,24,28,32,33,35,42,44,45,51,52,55,60,65,66,68,69,70,

%T 72,84,87,88,91,95,99,104,110,114,115,117,120,123,125,126,128,135,136,

%U 138,140,141,145,152,153,156,159,170,174,177,180,182,185,186,187,188

%N Numbers k such that the continued fraction of the harmonic mean of the divisors of k contains distinct elements.

%C All the harmonic numbers (A001599) are terms of this sequence.

%H Amiram Eldar, <a href="/A349502/b349502.txt">Table of n, a(n) for n = 1..10000</a>

%e 2 is a term since the harmonic mean of the divisors of 2 is 4/3 = 1 + 1/3 and the elements of the continued fraction, {1, 3}, are different.

%e 4 is not a term since the harmonic mean of the divisors of 4 is 12/7 = 1 + 1/(1 + 1/(2 + 1/2)) and the elements of the continued fraction, {1, 1, 2, 2}, are not distinct.

%t c[n_] := ContinuedFraction[DivisorSigma[0, n]/DivisorSigma[-1, n]]; q[n_] := Length[(cn = c[n])] == Length[DeleteDuplicates[cn]]; Select[Range[200], q]

%Y Cf. A001599, A349473, A349476.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 20 2021