A349474 - OEIS

%I #9 Nov 21 2021 05:08:48

%S 1,2,2,4,3,1,3,3,2,3,3,4,3,2,2,7,3,4,3,3,5,3,3,2,6,3,4,1,3,2,3,2,3,4,

%T 3,8,3,4,5,4,3,2,3,2,3,4,3,5,6,4,3,4,3,4,2,5,5,7,3,3,3,5,7,7,3,3,3,3,

%U 3,3,3,4,3,5,7,4,4,4,3,4,6,6,3,2,4,6,3

%N a(n) is the length of the continued fraction of the harmonic mean of the divisors of n.

%C a(n) = 1 if and only if n is a harmonic number (A001599).

%C a(n) <= 2 if and only if n is in A348865.

%H Amiram Eldar, <a href="/A349474/b349474.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 1 since the harmonic mean of the divisors of 1 is 1 and its continued fraction has 1 element, {1}.

%e a(2) = 2 since the harmonic mean of the divisors of 2 is 4/3 = 1 + 1/3 and its continued fraction has 2 elements, {1, 3}.

%e a(4) = 4 since the harmonic mean of the divisors of 4 is 12/7 = 1 + 1/(1 + 1/(2 + 1/2)) and its continued fraction has 4 elements, {1, 1, 2, 2}.

%t a[n_] := Length @ ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[-1, n]]; Array[a, 100]

%Y Row length of A349473.

%Y Cf. A001599, A071862, A099377, A099378, A348865.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 19 2021