A349474 a(n) is the length of the continued fraction of the harmonic mean of the divisors of n.
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, 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, 3, 3, 3, 4, 3, 5, 7, 4, 4, 4, 3, 4, 6, 6, 3, 2, 4, 6, 3
Offset: 1
Keywords
Examples
a(1) = 1 since the harmonic mean of the divisors of 1 is 1 and its continued fraction has 1 element, {1}. 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}. 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}.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
a[n_] := Length @ ContinuedFraction[DivisorSigma[0, n] / DivisorSigma[-1, n]]; Array[a, 100]
Comments